[Nick C]

I think it's fine. I'm not happy about the size of Villain's river bet, but it could be a frustration bet, and it is good for our chances that that ace wasn't there until the turn. (It also helps a little that the wheel draw was there, since Villain could have missed his gutshot but spiked a worse top pair instead.)

On the flop, I think a raise is all right. But so is calling, and really, I think I favor a call. A "free" turn card isn't a free card if we paid for it already with a flop raise that quite possibly was bigger than Villain's turn bet would have been, so it's mainly useful on those occasions when we catch on the turn and have thus built a pot for ourselves and disguised our hand. That is, I think the main benefit of a flop raise comes from the fact that we won't always want to take a free turn card and would prefer to make a sizeable bet instead. Villain's smallish stack size limits the benefit of this, though.

If we have any folding equity on a flop raise, then that's great too, but I'm not so optimistic about that in this particular spot.

If Villain is betting a worse draw, then a flop raise should slow him down, but we may still be in the awkward spot of facing a river bluff (after we check the turn) and wondering whether or not to call with ace-high. (And unless the river bluff is small, it's going to be hard to do that.) Meanwhile, if Villain just has a draw, a flop call could itself easily slow him down -- especially with that king on the board.

On the next street, raising the turn basically just seems bad to me (unless we have some reason to believe Villain will stubbornly call with, say, KJ or 77, and I don't think we do). There's a really good chance that Villain has, like, a 4-outer at this point, and he's not so deep-stacked that letting him stay in the pot is a major worry. Of course, if he's betting the turn as the last money he puts in the pot UI, then, sure, we might as well raise now, but I don't see why we should assume that's what's going on.