Hi Karen,
Richard Titshall and Sarah Fairweather did have a daughter Mary born 1796, Hacheston, Suffolk.
Could she have been known as Maria?
So William Gooch TITSHALL was born c 1816 to Maria ?
Married Jane, no Fathers name on Marriage Cert/ do you have it?
I noticed a family Tree with maiden name for Jane;
Was she Jane HOMAN?
Marriage, September 1843, Kensington, 3 305, William TITSHALL on same page is Jane Homan
(OOPS, just noticed name Homan on your surname table after I posted)
The only Edward Archer I can find, Blacksmith was possibly a Widower by 1841 unfortunately

1841 Census
Hasketon, Suffolk
HO107/1020/9/Hasketon
Edward ARCHER, 45, Blacksmith
Sarah, 13
Henry, 10
Trish
