This guy has a short stack, and IMO, the only time he's going to bluff is if he shoves on a scare card, putting us to a tough decision. He'd have to put 50%-100% of his total stack in there to bluff us. And he has a high likelyhood of a draw, and that has absolutely no showdown value if he misses. So he's less likely to bluff with that.
Because of his low probability of bluffing his hand on the river,...
The fact that this has no showdown value means that he is extremely likely to bluff the river, especially given his short stack. The purpose of bluffing with missed draws is to win a pot you have no chance of winning at a showdown = "one that has absolutely no showdown value". In fact, his turn check
tells us that he either has a draw and is slowing down, or he flopped a set, correctly led into our big ace that we raised with pf, and then checked knowing we'd bet our trips and he could instashove (AQ/AK probs would have 3-bet pf as many ppl have said (at length

) and would bet the turn protecting against fds I'm fairly sure as would any Ax where x is not 6 or 9, so this is probably not in villain's range). Basically this equates to a shove from him on the river on pretty much any card if we check behind on the turn: the full house will shove, the completed flush will shove, the busted flush draw will shove a lot of the time. If we were to check behind on the turn, on the river if no spade comes we have to pay off a full house imo, but if a spade (that isn't the jack) comes we have to fold it as there is very little we can beat.
If we shove the turn I think we do lose value from fds, as I think the >4/5 of the time the spade doesn't hit the villain will bluff-shove >1/4 of, making it a more profitable line than pushing on the turn, and seeing as the money is going to go in anyway against a fh checking behind on the turn > EV than pushing on the turn.
EDIT: when I say fd I probs mean fd or sd