You have a big hand against an unknown player without any reads. It can be anything because we don't know why this player keep check+calling. He can have JJ or he can have TP on the flop and looking to check-raise you on the river.
Anyway, your must be extremely lucky to extract 3streets of value with an over-pair. If villain is a moron with 99 he may call the river. Why not? - He called the Ten high flop, why not calling the river now. A weak fish will do that.
We have no idea what's going on without some very good reads after so much action.
First question is what would the SB raise with. In theory, it would be something of value. The call to your 3 bet validates that. So we can assume JJ-AA, AK, AQ, KQs, and maybe 9's or 10's. JTs is a possibility but unlikely.
Flop would hit his 10's, or his rare JT, and would appear that it missed A paint if he put you on that. So a flat call from him narrows him to T-A's, AK, AQ, and a club draw.
OTT, id check behind, he either made his flush, or is in the same position as the flop. A check from you controls the pot size so that if he did make his flush, it's cheaper on the river to call down a bet from him. There's no longer a draw to push him off of, so if he calls, he has a hand already and you're just bloating the pot.
OTR, if he has a made hand, he's probably betting out here shooting for value, it would be ballsy play to check and hope to raise a bet from you. At this point, with $1400 in the pot, it's a good win if you're ahead, and a bet here is gonna result in a fold and you winning anyways, or a raise that's gonna put you at risk for the rest of your money and a tough decision. Realistically, the only bet you have here is all in, is it worth risking what you have left?
I'm fine with how the hand was played up until now. May have sized larger on flop/turn, but whatever.
OTR I'm happy to be able to check to showdown and relieved that V didn't jam on us. The only hands we really beat are JJ and the naked Ac, neither of which should be paying us off. If by some chance he has some weird small 2p hand (which he shouldn't have anyway), he's now been counterfeited and isn't calling either. There's almost no hands that we're ahead of that will call a river bet.
