Coddenham might be interesting too.
Edward (abode Barham UH; late of Coddenham) buried 13 Jan 1850 age 65 Barham (sort of fits the Edward that Annes found).
Coddenham burials inc a Thomas Death snr buried 6 Oct 1771& on the same day his grandson Thomas appears to have been buried also.
Also Coddenham John Death buried 1765 & Susan Death buried 1776 sorry no ages or relationships given.
What I should have said in my last post is that all of the parishes mentioned are very close to each other.
Simon Fenn buried 2 Jun 1780 Baylham but interestingly there are only 2 early Death burials recorded on the SuffolK Burial Index at Baylham:
Sarah Death 20 Nov 1693 wife of William, buried in woollen
William Death 3 Aug 1698 Widower, buried in woollen.
The lack of Death burials in Baylham tends to suggest that your Thomas & Ann married in the brides parish & he was from elsewhere.
K