From a genealogy done by Rosemary St Leger-May with the title of "Hevingham of Heveningham and Ketteringham" (see http://freepages.genealogy.rootsweb.com/~heveningham/):

Possibly he was the son of Sir John Heveningham (d. 1499) of Heveningham and Margaret St Leger (poss. d. 1495) dau of John St Leger (1404-1442) of Ulcombe, Sussex and of Margaret Donnet.
George may have married Katharine Burgoyne, dau of John Burgoyne and had two daus Anne and Alice, presumably co-heirs.