The next logical step is to look at all the Thornton marriages for both Richard and John Tatham in the late 1500s. There records don't cover that time frame.
JOHN
John Tatham Anne Tatham 27 April 1635
John Tatham Anne Wildeman 28 April 1635
RICHARD
Richard Tathame Ellen Robinson 16 January 1592
Richard Tathame Elizabeth Beamonde 8 December 1594
Richard Tathame Elizabeth Hollme 28 May 1598
Richard Tathame Agnes Grenefell 30 July 1598
Richard Tathame Elizabeth Gibson 16 May 1601
and none show any reference to Bigcroft.
so: In order... I have covered
1) Burials
2) Baptisms
3) Marriages
There are very many other Tatham family in the Thornton registers but I was trying to stay focused only on Bigcrofte and
John Tathame of Biggecroft
Robert Tatham of Biggecrofte, Yorkshire
Jane Tatham
Margaret Tatham