heads-up and OOP with K9o

[n.s.]

live 10-20

villain (button) is a tight, decent player. He's a bit on the passive side, but he will adjust for things like steal-resteal situations. He doesn't bluff very often, but he's not incapable of it. He's friendly and not the actor type at all. He probably sees me about the same way that I see him.

Earlier in the evening he did make one questionable play, though. He raised PF from LP, checked through a two-tone board (multiway), checked through the turn when he made TPGK (he had none of the flush cards) and raised a river bet on a blank river.

Fold to me in the CO and I raise K9o, villain 3-bets, blinds clear out, I call.

Flop: 567r
I check, villain bets, I call.

Turn: 9
I check, villain thinks for a bit and bets, I raise, villain calls relatively quickly.

River: blank
I bet, intending to fold.

Standard? Should I just bet the turn? Is c/f (or even c/c?) better on the river?