An extensive biography is found in this source (http://balder.prohosting.com/shissem/Hissem_Robert_Heysham_Branch.html) Following are brief excerpts:

William Heysham, whose father was William Sr., was christened on 26 February 1721 in Saint Mary's Church, Lancaster, Lancashire, England. He came to America in the mid-1740's with his brothers, Thomas and Christopher, initially settling in New York City. He was a ship's captain and merchant.

As mentioned in Christopher Heysham's biography, above, William married "an American lady whom he met on one of his former visits [to an American port while still a merchant in Hull, England]." William married Mary Oaks in New York City on 3 May 1752 in Trinity Church Parish, New York City. In some sources he is shown to have married Mary circa 1755 in Philadelphia. This may be a simple misunderstanding based on William and Mary's later residence in that city. Mary was born in 1723 and died on 24 [or 27] March 1791 in Philadelphia in the 68th year of her life.

William was, while living in New York City, in the employ of two New York City merchants, George Folliot and James Depeyster.

Beginning in 1756 William ran into a long series of misfortunes that led to his moving to Philadelphia. First, he lost the CHARMING SALLY in a wreck off the coast of Florida. From the "New York Mercury" of 2 August 1756. William then had another ship, the JEVON.

William fled New York City in 1759/60. I do not know where he was for the next five years, but by 1765 he was residing in Philadelphia.
William was not one of the major merchants of Philadelphia. He, like most, probably ventured only one voyage a year, or every other year. Ten merchants/firms controlled over 50 percent of trade.
In July 1765 William became a member of the Society for the Relief of Poor Distressed Masters of Ships, their Widows and Children." - from "Some Account of the Tree Family" by Josiah Granville Leach. See a post-war reference to William's continuing role in the association, below.
An early patriot, William signed the "Code of Honor" or Non-Importation Resolution of 25 October 1765 of Philadelphia in which the signers agreed not to import any British wares, a demonstration that helped lead to independence.

William was a member of the City Committee of Correspondence, probably starting in 1774. Committees of this sort were first proposed by Virginia in March 1773 and tasked with contacting the legislatures of each colony so that they could join Virginia and offer concerted opposition toward British encroachments.

William Haysham [sic] made his oath of allegiance in 1777 - from "Names of Persons Who Took the Oath of Allegiance to the State of Pennsylvania," by John B. Linn and Willima H. Egle.

As inevitable occupation neared, William Heysham assisted in removing the chime of bells from the Christ Church tower. Note that "Vestrymen at Christ Church hesitated to remove the church's bells because of the expense involved, and as a result, Pennsylvania's commissary generals took seven bells from Christ Church and two from St. Peter's." - from "Old City Philadelphia: Cradle of American Democracy. Does this mean that William was a commissary general? His later career seems to imply that. Christ Church's Bells are one of three rings of bells which were installed in the United States prior to the American Revolution. The Bells were cast by the foundry at Whitechapel, England owned by Thomas Lester and Thomas Pack, the same firm which first cast the Liberty Bell two years before Christ Church's bells were cast in 1754. The bells of the church were rung on 8 July 8 1776 to announce the first public reading of the Declaration of Independence. A few months later the Liberty Bell and the bells of Christ Church were removed and hidden in Old Zion Reformed Church in Allentown for safekeeping during the invasion of Philadelphia. The bells were returned and re-hung in August of 1778.

What happened to William during the nine-month British occupation? As a well known patriot both his life and property were at risk. He had been in positions of authority whose intrusive nature and prospective impact on other's income and property was so profound that he must have angered many who would be ready now for revenge. There is no indication from the information above, however, that William was planning to leave the city. Note also that none of the tax reports for the city and province show any indication that he owned land, so there was no 'country estate' for him to escape to. Others did make plans. Charles Willson Peale, an acquaintance of William's, spent the last days before the British arrival finding a refuge outside Philadelphia for his family. He then rejoined the American forces. William may have done something similar, finding a sympathetic associate in the country to watch his family, while he shifted for himself. I have recently found the following that notes William's arrest on the first day of the occupation.

On 12 October 1779 William Heysham was listed as an Assistant Judge of election returns, along with Benjamin Paschall and William Adcock, and assorted inspectors, Freeholders of Philadelphia. They attested that George Bryan, Michl. Shubart, William Hollingshead, Jacob Schriner, and Charles William Peale were duly elected Representatives in the General Assembly for the city of Philadelphia. On the same day they attested to the election of William Moore, Esquire, as Councellor for the city.

On 27 May 1780 William Heysham was listed as an Assistant Judge of election returns, along with Benjamin Paschall and William Adcock, and assorted inspectors, Freeholders of Philadelphia. They attested that James Hutchinson, Esquire, was duly elected a Member of the House of Representatives for the city of Philadelphia.

William resided on the north side of Mulberry street, between Third and Fourth streets in Philadelphia. Mulberry Street was called Arch Street early on; the reason-- that Front Street formed an arch or bridge when it passed over Mulberry Street, with the latter going down to the riverside to form a public landing-- this ceased to be true in the 1720s. The name nevertheless stuck, long after most people had forgotten the arch itself.

William was elected a member of the Society of the Sons of St. George on 23 April 1793 - from Theodore M. Banta's "Sayre Family," 1901, and based on information from the family Bible of William Heysham Sayre, William's great-grandson. Note that William's sword, per Banta, was in the possession of William Heysham Sayre, in South Bethlehem, Pennsylvania. Another descendent, the Reverand Theodore Heysham, claimed the sword was in his possession, though he may have been referring to the sword of William's son, Robert.

William died in Philadelphia on 26 September 1797 at the age of 77.