Had a look at the various generations, starting from your grandfather (what a gift of a name to research). you probably have most of this already, but here goes:
Got as far as Ann(e) Annats b abt 1790 Clatford, Hants (source 1851 census). When she married Silas Stone in 1808 she was a minor (under 21). One of the witnesses was John Annats. Ann could sign her name, John made his mark. Most likely baptism is Ann Annats - 10 jan 1790 base born daughter of Mary Annats at Clatford. The most likely baptism for Mary is d/o Henry and Jane on 30 oct 1766 at Clatford. This couple also have a son John bapt at Clatford on 5 Aug 1777.
Can't find what happened to Mary, but brother John (Ann's uncle) turns up in Winterslow married to a Rebecca.
1851 census Piece number 1846, Folio 17, page 26. Confirms birth town Clatford and age 73.
John Annets married rebecca Collins at Winterslow on 26 May 1806. John Annetts made his mark, Rebecca and two Collins witnesses signed. One witness was Alexander Collins, John Annets called a son Alexander.
John Annets witnessing Ann's marriage to Silas, might be a way of him (her uncle and possibly guardian) giving consent to the marriage. Mary may have died by then or married and kept her previous illegitimate child a secret.
Many trees have Ann's parents as Edward Annats and Mary Hillier, but I cannot see any evidence for that whatsoever.
