[Lmn55d]

I don't like either. In hand 1 if you're gonna check the turn you gotta call that river. There's just too many draws or random hands he could be bluffing. I like the turn check if you fear a semibluff/bluff turn checkraise and/or think you will induce a river bluff at a very high frequency. Otherwise I would bet/fold turn.

Hand 2 when he checks the turn he is either going for a checkraise, has a hand that he wants to go to showdown with cheaply, or is giving up. I think the first 2 categories are a lot more likely than the second, so I think you should check and hope to pair on the river. I don't hate your turn bet if you think the 3rd category is likely.

I do hate the river bet, however. Usually when he check/calls that turn it means he's showing down his hand. He's not folding a pair and if he does fold, it usually means you had the best hand anyway with jack high.