Simon Everett/Everitt, b. abt 1670/1673, VA. Married Ann Turner (b. abt 1676, Isle of Wight Co., daughter of John Turner and Mary Tomlin) abt 1695, Isle of Wight Co., VA. I am related through their son Simon and Miss (Elizabeth or Sarah Vasser, married about 1721, Isle of Wight Co., VA.
I am also related to Ann Turner through her brother Joseph Turner, born abt 1678/83, married to Burchett Lundy about 1708/1710, Isle of Wight Co., VA. I have done extensive research on the Turner line. I've had more trouble, though, verifying the Everett/Everitt line.
You have your Thomas born about 1700 in Southampton Co., VA, as son of Simon and Ann Turner, who never lived in Southampton Co. Simon and Ann's son Thomas died in 1723 (will 9 Oct 1723/ probate 27 Jan 1724, Isle of Wight Co.). He mentioned a wife (her name not included) but no mention of any children/orphans left behind. He died fairly young.
There were several Everitts/Everetts in the area, no doubt related probably back in England, with different spelling veriations popping up after they immigrated to America. There were even some Simon Everetts in Massachusetts at that time! I believe that your Thomas is probably related to the line, but I don't know enough about the family to be able to tell you where.
I've though that maybe Simon was related somehow to William and Ann (Simon/Symon ?) Everitt, but he would have to have been a grandson. Maybe Simon's father was a brother to a Simon who was actually your Thomas' father. And you write that your Thomas had a brother Simon, also. My Simon had a son Simon, who I am also related to, and he also had a son Simon. Whew!