Villian was an unknown at the time.

PokerStars No-Limit Hold'em, $10 BB (5 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP ($1585)
Hero ($1078)
SB ($1010.50)
BB ($910.10)
UTG ($2403)

Preflop: Hero is Button with 3, A.
2 folds, Hero raises to $40, SB calls $35, BB calls $30.

Flop: ($120) A, 2, Q (3 players)
SB bets $60, BB folds, Hero calls $60.

Turn: ($240) 3 (2 players)
SB bets $60, Hero raises to $275, SB calls $215.

River: ($790) 4 (2 players)
SB checks, Hero

I'd check here. Pot is big enough to take down with the best hand, if you have it. If you make a bet here and get raised a decent amount, I can't see a call anyways.

I don't see a reason to think that card changes anything, other than A4 or A5 what other hands beat you now that didn't beat you already? I think it's much more likely that he has AT or AJ.

The only reason I'd be hesisant to bet the river is if I think he could have AQ or better and is looking for a check-raise on the river.

Yeah, the pot may be getting to be a decent size, but that doesn't matter. What matters is that the hero likely has the best hand and the villain often has a hand that he will pay off another bet with. To fail to make that bet is a pretty big error.

I don't think the villain is trapping here. If he had 5x of spades or A5 then I think he'd lead the river again.

Honestly, the only hand I'm really worried about here is A4. You're repping AQ pretty strongly here and if the villain had A4 and stuck around hoping to hit his gutter, he might still be worried that his aces up are no good.

I think a value bet of about $300 will show a very good profit in the long run becuase the villain will likely call with any ace, and it appears that he's holding a hand like AT or AJ.

I agree that he probably ahead. But as with any 2 pair, a large raise in front of you might mean a difficult decision.
Villain probably didn't flop top two, because of the size of his weak flop/turn bets. He probably has a weak ace and is try to see it as cheaply as possible. This puts his range, like you said, at a hand like A4 - or even hands like A-5 or A-6.

This means villain could be throwing out protective bets since he has the lead, and calling raises like he did on the turn. When the 4 hits, A-3 suddenly isn't looking as pretty as it did. Say hero value bets $300 and then villain pushes for his last ~$400 more. Hero has to make a crying call with a terrible board (at the river), or make a fold and throw almost $600 away.

Checking here guarantees that if we have the best hand we take the pot, without having to make tough decisions.
If we get lucky, villain calls with the worse hand.

Just how I see it.

This isn't a terrible board. The only 3 likely hands to beat us are A4, A5 and any spade draw that had a 5 in it. The river didn't really change that much. Yes, we're now losing to A4 and A5, but if we bet $300, we'll get called by A6-AJ and even if the villain has A4, he can't reraise our value bet on the end. The only hand that he could come over top with is an unlikely set, or the straight. As played, the Hero's hand seems even stronger than it is and he could easily have top 2 or a set of As or Qs. The hero check-raising on the river is unlikely with any holding that doesn't have a 5 in it, and if he did have a 5, he would likely bet out or push the river since our hand already seems so strong that it is unlikely that he would lose his customer.

Seems like an easy value bet to me. The villain's bet on the turn seems weak and defensive. I think he has about A J, or A T.

Ditto Acid.

Word

Easy value bet..It would be more of an issue if the river came a 10, J, or spade