I haven't found anything further about my William. I think this may be him. An entry in the parish registers in Cotton, for 1744 - William base child of Elizabeth Davey, baptised 22 November. Cotton is apparently near Wickham Skeith. There is a William Davy born about 1745 in Wickham Skeith Suffolk listed on the IGI film no. 1985530. No parents listed. However the parish records do not have an entry for William at Wickham Skeith.
I have another Davy family (eventually marries one of William's descendants)one day I think there will be a common ancestor. With this family Mary Davy (bapt 13 July 1766 Rumburgh, Suffolk) married Robert Reeder ( bapt 27 Aug 1769 St Mary Magdalene Norfolk) in 1790 Rumburgh, Suffolk. Mary's parents were Samuel Davy ( 1733 Bungay) and Elizabeth Reynolds(abt 1741/2 ?) - I do not have details of their marriage, or Mary's siblings.I don't know if this is of any help - but may give you some places to look for your Davy family.