John Weston

The History of Parliament page for Robert Weston lists John Weston and Cecily Neville as his parents and says: "Although the published pedigrees disagree as to whether Cecily Neville was Weston’s mother or grandmother, what little is known about Cecily establishes her identity with Weston’s mother. PCC 25 Peter; N. and Q. (ser. 4), iv. 367; Emden, Biog. Reg. Univ. Oxf. 1501-40, p.618."
The History of Parliament is an extremely reputable source that for decades has conducted extensive research on historical members of parliament, and if they have concluded that Cecily Neville was the wife of John Weston and the mother of his children, then I think that's fairly convincing. The main objection I've seen to identifying Cecily Neville as John's wife is that it seems unlikely that the daughter of Ralph Neville would have married someone of John Weston's social status. But the researchers at History of Parliament, who have studied and researched British history for years, apparently don't think it's that unlikely.

Source: The History of Parliament: the House of Commons 1509-1558, ed. S.T. Bindoff, 1982. Link to entry in online database: https://www.historyofparliamentonline.org/volume/1509-1558/member/w...)