tl;dr: Meh, I call.
Knowing more about the opponent would help, but let's assume you don't know anything about their style of play. Since they call a raise, you can narrow their preflop range, but for random players defending their big blind it might not be as narrow as otherwise.
On the flop, I see their betting range as reasonably being any ace, including two pair, sets, 44, 55, two hearts, and once in a while a total bluff or something like 56ss. Since you call the bet, the small blind should put you on at least an ace, but possibly a floated pocket pair or something--this is where knowing what level of thinking your opponent is on helps.
They check the turn. The offsuit ten is unlikely to have helped any of their possible holdings. On the other hand, it's unlikely to have helped you either, so whatever reason they had to bet the flop (like protecting against a draw) should apply to the turn also. You've showed interest in the hand and might have an ace, so why not continue to bet their strong hands here? That is, unless they are so confident in their hand and that you have something that they expect you to bet or they want to keep you in for a river bet--this is the riskiest situation we might be facing. What if they have a medium strength hand like Ax though? A check now makes sense. What if they were bluffing or semi-bluffing before? A check also now makes sense. With all those scenarios, it looks most likely that they don't have the strongest part of their range.
With the Q on the river, the only real hand of theirs that this changes anything for is if they had KhJh, QhTh, or any AQ (you were already beat, but they will be more confident in it now). With these hands, or AT, or something like a set that they tried to trap with on the turn, the opponent will be betting and everything makes sense. A hand like AJ or A8 which they might have bet the flop with but checked the turn with probably shouldn't be betting the river, but rather check-calling, but that varies by player--still I wouldn't give much weight to this part of their range. Now, if they were bluffing or semi-bluffing on the flop, their hand hasn't improved, and they see that you didn't take the opportunity to bet the turn (you also didn't raise the flop)--this would be a legitimate opportunity for them to throw out a half-pot size bet as a bluff to see if your hand is really strong enough to face the bet. They may think you can fold something like JJ here or you missed a flush draw so it's worth a try. I don't ever see a worse hand than yours betting for value though.
With all that, I would call because you are getting roughly 3:1 and therefore need at least a 25% chance of winning. You can realistically label part of their range as a bluff as the "story" would fit, and the "strong" part of their range that beats you is sufficiently narrow enough that it's probably profitable for you. In close calls like this might be, I would start off erring on the side of calling because not only do you have the chance of winning, but you'll get valuable information about your opponent that you can exploit later, especially given your relative positions at the table.
