Edward Waterman, senior and his wife Jane are both buried in Hintlesham:
Edward Waterman bc.1777 bur.28/4/1841 Hintlesham (died 2 months before census)
Jane bc.1788 bur.15/1/1869 Hintlesham.
Jane thus still alive in 1841/51/61 census when birthplace given as Hadleigh, Suffolk
Think that Edward bc.1777 was probably born in Hintlesham but early records for Hintlesham are not available online.
The only 2 early burials I can see in Hintlesham are:
William bc.1745 buried 24/6/1796
Mary bc.1741 buried 27/4/1824
If he was indeed born at Hintlesham then this couple seem to be the likely parents:
William Waterman of Hintlesham, married Mary Allen 25/12/1770 Sproughton, Suffolk (marriage on FindMyPast)
In 1851 Census at Hintlesham (ref.HO107-1798-37-16)
Jane Warterman 64 born Hadleigh Suffolk
John Willis 44 son born Layham, Suffolk
+ 2 lodgers
This would support the marriages found so at least one son born from her first marriage.
As far as I can see from online records at familysearch Edward and Jane had the following children (although seems to be gap between marriage in 1812 and 1st known baptisms in1818):
Edward bp.22/3/1818 Hadleigh )
Mary bp.22/3/1818 Hadleigh ) twins perhaps
Eliza bp.10/12/1820 Hadleigh
Martha bp.5/9/1822 Chattisham, bur.22/9/1822 Hintlesham
George William bp.9/4/1826 Hadleigh
Susanna bp.1/6/1828 Hintlesham
Sarah bp.14/2/1831 Hintlesham
Annette