I would find it tough to fold the river after playing it this way, with the odds
your getting. But theres not a ton of hands you are legitamately beating that he value bets here. Maybe like 99-TT, any other 1 pair hand worse than that I would think most people would be happy to check back for showdown.
I'd prefer double barreling on the turn instead of check calling. There could be some pair + straight draw hands in his range (89,87,67) or 9T. If you check to him and he checks back youve probably missed value, if he bets your going to have to play a guessing game on the river for a larger bet potentially. So whether he calls or raises your turn bet is going to tell you a lot about his hand