Stacy Waterman is mentioned as a son in the 1820 will of Betsey Gorton. He is also mentioned in the will of Sarah (Latham) Knight 4 Feb 1832. Sarah's will also mentions by name his three daughters: Ann Eliza, Amey G., and Mary.
Stacy was an auctioneer in Johnston, RI. He held many civic positions in town between 1814 and 1839.
In 1839 he moved to Conklin, NY, where he bought land that year but lost if to foreclosure in 1842. The family is back in Cranston, RI, by the 1850 census.
For more information on this family, see "The Waterman Family" by Edgar Francis Waterman, at Google Books.