This profile of William Stone and his family associations appears to be a mixture of two or three different William Stones.
The William Stone who married Margaret Dix and had daughter Mary Stone who married Abraham Tappan seems to have not yet identified parents. That William Stone married Margaret Dix 18 August 1696 in Woodbridge, New Jersey (noted in the text Woodbridge and Vicinity by Joseph Dally, 1873). There are three recorded children from that marriage, all born in Woodbridge: Mary born 6 August 1697 who married Abraham Tappan; Samuel born 1698 who married Rebecca Bloomfield; and William born 1700 and died 1788 -- this son William also married a woman named Margaret (last name unknown) -- his wife died about 1737 and he remarried Lucy Walker in 1758. The William Stone who married Margaret Dix in Woodbridge may have died in 1703; the reason to think this is that there are only these three recorded children (Mary, Samuel, and William) and there is a New Jersey probate record for William Stone for 1703 but the record is only his inventory so it is not sure if it is this same person.