Janice -- You are right that there doesn't seem to be much information around on this person! What is your connection to this family? (Mine is the Southwell line via son Ebenezer.) I have found a few items that you didn't mention:
Northampton [Massachusetts] Register of Deaths says William died 19 Mar 1723.
Findagrave.com has a photo posted of his gravestone at the Bridge Street Cemetery of Northampton: "Here lyes interred the body of William Southwill who dyed the 19 day of March in the 64 of his age in the year 1723".
His daughter Sarah married Daniel Hubbard 18 Dec 1716 Northampton.
His wife Sarah married second, 3 Jul 1733 (Suffield Connecticut VR), Deacon John Hanchett whom she survived as his 4th wife.