[1] Through his paternal side, he was a descendant of Colonel Edwin Conway, a member of the Virginia House of Burgesses.
[3] In 1752, Conway was one of the benefactors of the Alexandria Town Hall and Court House, along with John Carlyle and William Ramsay.
[4] Conway was the owner of the shipping vessels Molly and Betsey which operated on the U.S. East Coast.
[6][7] In March 1789, he lent £625 ($95,000 in 2023, adjusted to inflation) to Washington one month before he assumed the Presidency to settle some Virginia debts and fund his trip to Federal Hall for his inauguration in New York.
[11][12][13] Shortly after his term as mayor, Conway presented grievances to the Virginia General Assembly regarding foreign trade policy, which helped lead to the Mount Vernon Conference of 1785 which governed state rights on the Potomac River, Pocomoke River, and Chesapeake Bay.