Full house possible. His overpair I don't think so, because he should raise pre flop.
Pre flop: IMO check is good. He limps, so IMO he could have small pocket pair like: 44, 66, 77 we know that. After flop he raises you. It looks like he try to protect his hand (set?) before maybe your FD. He could think that you play donk bet and you have FD IMO, so he don't want a flush on the turn. Turn is 6d. Possible full house for him, he bets small bet, he try play some value or wait on your move. On the river I check and wait on his move, if he plays more than 2/3 pot I fold, if he bets less than 2/3 pot I risk and make a call. (Sorry for my english) Otherwise I'm curious other opinions.