I think cbetting here is fine, and checking back is also fine, the latter being a little better as the board is fairly dry and there aren't too many turns that make us regret cbetting.
He doesn't have much value here, only two value hands (being the sets). Usually this is a gut shot or a random bluff and there are lots of GS combos even with us blocking some. I'm perfectly happy calling here and re-evaluating ott. Folding here is awful imo. Probably not folding the turn, either, since there's a decent chance his gut shots will simply pair up. If he barrels river then we can seriously think about folding.
EDIT: Also, I'm not sure how often he x/r with sets here since the board is dry, sure the K is in our range but we also miss this flop a lot which makes me think he is very likely bluffing here with a GS at best for him in terms of equity. Call and be happy to.