Normally I'd say bet, especially against the typical calling station. But if this player is a little tricky and he regards you as a pretty straifgtforward tight player I think a check is better. If he was just planning to call down a small pair because he thought there's a good chance you're playing big cards he'd probably fold a river bet (how could you have missed with two big cards?).
I'd say you lose less if he has a flush, aces, kings or a slowplayed big hand and checkraises/calls you than you win if he has a small pair and calls you. And there's of course a slim chance that he will try to bluff you or bet with a weaker hand (value betting a small pair) when you check. So I'd say check/call river. Other streets are fine.