[Lmn55d]

I would bet the turn unless you expect to get semibluff-raised or bluff raised pretty frequently. In the games I play, most guys will call down with any pair here. He also could have peeled the flop with 56 or 67 (or a flush draw in example 2).

If he calls the turn, I would also bet the river and fold to a raise. I think you miss too much value by checking the turn.

If it's a very aggro guy who is capable of raising as a bluff or semibluff, go ahead and check it. Or if it's a guy who will only call the flop with an ace.

Otherwise, bet it dawg.