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What did you put Villain on in hand #1. The re-raise should limit him to only a few hands AA-JJ and AK. The .50 bet into the $7 pot after the flop seems like a weak player testing whether you have an Ace that beats his PP. Slow playing here lets too many draws see free cards on the turn with both a flush draw and straight draws on the board. I'd have raised this turn.

The $15 turn bet after the low flop bet makes me think he hit his set of Kings and is afraid of the flush and straight and wants to take it down here. Either way, every hand but QQ that he would have re-raised with now has you beat. After the river card, all these hands have you beat. Check the river, but you already know that.

Hand #2... I'd only check this flop if I had a read on villain and knew he'd fire at the pot to check-raise him. Villain raised preflop, so chances are he will a PP or hit part of this flop. If he has a PP, you're just giving him a chance to make a set. Most players at this level won't fire with a PP with big overs on the board and a re-raiser. If he hit part of the flop, he'll call your bet, anyway. Just fire.

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For hand 1, going back and reading it, I think it was pretty misplayed. A better line would be to raise the flop. I guess from his underbet, I figured him for a smaller pocket pair. On the turn, why would he overbet the pot with a set of kings? Something that strong would likely slow down or at least bet less than $15. I figured him for QQ at this point. No idea why I bet the river, that was horrid.

For hand two, even though I give him a chance to hit the set, I think he'll put enough money in when he doesn't hit for a slowplay to be the most +EV.