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The "Act for rebuilding the pier and harbour of Parton, in the county of Cumberland" was first introduced as a Bill in Parliament on 9 Oct 1722, and eventually passed into law on 12 Nov 1724. This abstract and partial transcript is taken from the copy in Whitehaven Record Office (ref. DH532/1). This second Parton Harbour Act (the reasons for which are explained in polite terms within its text) refers back to the first, also summarised on this website. At the end of this page you will also find a summary of the Act of 1731/2 extending the powers of this second Act.
(NB: in these summaries, ... indicates text I have skipped)

"Whereas by an Act of Parliament passed in the fourth and fifth years of the reign of her late Majesty Queen Anne... a duty was laid upon all coals shipt or put on board any ship or vessel in the said pier and harbour at Parton for the term of eleven years, for and towards enlarging, deepening, cleansing, maintaining, and repairing the said pier and harbour: and whereas the term, for which the said duties were granted, is since expired, and several of the Trustees, who were appointed by the said Act for putting the same in execution, living remote, others very little concerned, or interested, in the preservation of the said harbour, and several others being dead, the works of the harbour were neither built nor kept in repair as they ought to have been, but have for some years past been wholly neglected, and are now become ruinous, to the great damage of the inhabitants there, who had built houses upon a prospect of a considerable trade in exportation of coals, and other the produce of the country, from the said harbour, to the loss of the coal-trade, and of His Majesty's Customs there: for remedy whereof, and for preventing the utter loss of the said harbour, Be it enacted... That all and singular the duties upon coals, by the said recited Act granted, shall be revived, continued, and paid, from the first day of May, one thousand seven hundred and twenty five, for the term of fifteen years....
And whereas the perpetual duty of one farthing, granted by the said recited Act, is found by experience not to be sufficient for that purpose, be it further enacted... that from and after the first day of May, one thousand seven hundred and twenty five, the same shall utterly cease and determine; and that, in lieu thereof, every master or person, who shall have the rule or command of any ship or vessel, shall, from and after the determination of the said duties hereby granted for fifteen years, pay one half peny for every one hundred ninety two gallons of coals...
And whereas it is necessary that the bounds and limits, of the said harbour should be ascertained and known, Be it enacted... that all that precinct, included within the limits and bounds herein after mentioned (that is to say) beginning at the north corner of William Watters's ground-plat, near the end of the Old Pier, and from thence along the present walls on the north-west side of the several ground-plats of the said William Watters, John Mathews, and Henry Walker, to the south-west corner of the said Henry Walker's garden, fronting to Mathew Jackson's house, and from thence, in a line running west to the low-water mark, from thence by the low-water mark, till it intersect a line running north-west from the north corner of the summer-house of Thomas Lamplugh Esquire, and so along the said line to the top of the beech, from thence along the height of the beech, till it reach the present counter-mole, from thence by the line of the said counter-mole, to the range of the wall inclosing the north-west side of the ground late of Anthony Whiteside, from thence along the said wall, to the west corner of Jacob Sunton's ground, from thence along the west wall of the said Jacob Sunton's ground, till it meet with the street before the front of Nathaniel Lowes and Peter Walker's houses, from thence by the north-side of the said street (leaving the distance of ten yards before the fronts of the houses for the breadth of the street) till it intersect a line drawn at eight yards distance before the front of William Watter's house, and parallel thereto, and so along the said line in front of William Watter's house, till it intersect a line in the range of the north-west wall of William Watter's ground, and from thence to the north corner of the said William Watter's ground-plat, where it begun, is and shall be from henceforth for ever the harbour of Parton aforesaid.
And be it further enacted... That there shall be paid, for all goods and merchandize herein after mentioned, which shall be landed or discharged out of any ship or vessel in the said harbour coming coastwise from any port in this Kingdom, from and after the said first day of May, one thousand seven hundred and twenty five, for and during the term of fifteen years aforesaid... for every hogshead of tobacco, three pence; for every hogshead of sugar, six pence; for every tun of wine, brandy or other exciseable liquors, two shillings; for every tun of hemp or flax, eighteen pence; for every hundred of deals, eight pence; for every last of pitch or tar, eight pence; for every tun of iron, one shilling; for every tun of raft or other timber, four pence; for every barrel of herrings, one peny; for every pack of linen, containing two hundred weight, computing one hundred and twelve pounds to the hundred, one shilling... all which duties shall be paid by the merchant, or other person, into whose custody or possession, or by whose order the said goods and merchandize brought coastwise, as aforesaid, shall be delivered.
And be it enacted... during the term aforesaid, every master, or other person or persons, having the rule and command of any ship or vessel, shall pay for every such ship or vessel, upon her arrival at the said harbour from any port or place of her last discharge in Europe, other than the kingdoms of Great Britain and Ireland, and the Isle of Man, the sum of four pence per tun; and for every such ship or vessel, upon her arrival at the said harbour from the port or place of her last discharge in Asia, Africa or America, the sum of eight pence per tun...
Provided always, That for every ship or vessel, which, during the term aforesaid, shall by stress of weather be drove into the said harbour or Parton, or shall otherwise come into the same for security or preservation, and not for discharge, there shall be paid one fourth part of the aforesaid duties of tonnage..."
After the 15 year period, tonnage duties payable to be 1/3 of those above, for ever.
"And whereas it is necessary that a considerable sum should be immediately advanced for buying and laying in materials for the said pier, and a further sum for building and finishing the same, be it enacted... That John Brougham, Esq; Lord of the Manor of Moresby, his heirs and assigns..., James Lowther of Whitehaven, in the county of Cumberland, Esquire, his heirs and assigns; the honourable Anthony Lowther, Esquire, Sir Christopher Musgrave, Sir Wilfred Lawson, Baronets, Sir Thomas Pengelly, Knight, Gilfrid Lawson, Henry Aglionby, James Bateman, Joseph Pennington, Peter Brougham, Humphrey Senhouse, and Richard Gilpin, Esquires, John Spedding, Joseph Richmond, Thomas Lowson, Peter Walker, William Graham, Mathew Jackson, Joseph Steel, and Nathaniel Lowes, Gentlemen, shall be, and are hereby appointed Trustees in lieu and instead of the Trustees appointed by the said recited Act; and that they, or any eight or more of them, shall have full power to put this and the said recited Act into execution..."
The Trustees may pay collectors up to 12 pence in the pound;
may make contracts with workmen;
may borrow, by mortgaging the duties collectable, up to £2000 at up to 5% interest per annum;
if all the work except ongoing repair is completed before the 15-year term expires, then the perpetual rates come into effect;
collectors may distrain goods for non-payment of duties;

" person or persons whatsoever shall, at any time, dig or take away any stones from any rock or quarry, which shall be within forty yards of the west-side of the said pier or harbour, under the penalty of ten shillings for every cart-load of stones so dug or carried away.
And for the better preserving the said pier and harbour from annoyances, and from being choaked up, be it further enacted... That no ballast shall be unloaden from any ship or vessel, into any keil, lighter, boat or cart, within the said pier or harbour, without a sufficient port-sail, duly fixed and spread, under the penalty of twenty shillings, to be paid by the master of such ship or vessel, or other person so unloading the same; and that no part of such balast so unloaden shall be thrown out, till it be within thirty yards of a ballast-post, to be fixed by the said Trustees for that purpose, under the like penalty of twenty shillngs, to be paid by the master of such ship or vessel; that no person shall heave, or deliver, and stones, sand, gravel, ashes, dung, rubbish, or other annoyance, into the said pier or harbour under the penalty of ten shillings for every such offence, and under the like further penalty of ten shillings, if the same be not forthwith removed, upon notice given them,by any one of the Trustees... or by the person who shall be appointed collector or receiver of the said duties; that if any ship or vessel shall, through mismanagement or carelessness, run foul or bulge upon the pier or mole belonging to the said harbour, whereby the same shall be in any way damnified, the master or ruler of such ship or vessel shall, with all convenient speed, upon notice as aforesaid, repair the damage so sustained, at the charge of such ship or vessel, under the penalty of double the value thereof, for every such neglect."
Further clauses:
all fines & penalties listed above (except the expenses of getting them paid, or as decided by a quorum of Trustees, rewards for information) must be added to the harbour maintenance fund;
all the penalties may be recovered by distraint on the offender's property, by warrant from a Cumberland JP;
Trustees must meet at least once a year, on the first Monday in July;
on the death or resignation of any trustee except John Brougham or James Lowther, a replacement must be elected within 60 days;
General Issue/ public Act clause at end as usual

"An Act for enlarging the term granted by an Act made in the eleventh year of the reign of his late Majesty King George the First, for rebuilding the pier and harbour of Parton, in the county of Cumberland" was introduced as a Bill in Parliament on 23 Jan 1727, and passed into law on 13 Jan 1732 (=1731 in the old calendar).

Reciting the terms of the second Act, it states that the Trustees "have borrowed the said sum of two thousand pounds, upon security of the said Duties, and applied the same to the rebuilding the said pier, whereby the harbour is capable of receiving several small ships, and from which there is a frequent exportation of coals to Ireland, and other parts: And whereas, to make the said harbour complete and capable of receiving more ships, and of greater burthen, it will be necessary to add several yards to the foot of the said pier, and for cleansing the said harbour, and carrying away and keeping the same clear of sand, it will be necessary to bring and cause a small brook, called Morresby Beck, running near to the said harbour, to run into the same; all which cannot be done, unless the said Duties be continued for a longer term, and the Trustees impowered to borrow a further sum upon the security thereof: Be it therefore enacted... That all and singular the Duties granted by the said Act shall be continued and paid from and after the expiration thereof, for and during the further term of twenty one years from thence next ensuing....
the said Trustees... may borrow any sum or sums of money, not exceeding the sum of two thousand five hundred pounds" at not more than 5% annual interest. As before, if the loan is paid off early, the lower duty rates come into effect.