Btw you can't bet pot on the river. You'll have $5.95 left and there'll be $9.75 in the pot. If you happen to hit the straight on the river you are certainly all-in.

I'm not sure I'd put him exactly on 77-TT. There's really no reason why he shouldn't be playing a set in this way. A small raise could be one wanting you to call rather than fold - as in, a strong hand like a set, or as you suggest a small overpair. It's true that many people at these stakes illogically bets/raises small with weak made hands, whereas with a bigger overpair he'd be more inclined to price out draws correctly.

When you make the call you need to have a plan for the hand according to PNL's coverage of commitment thresholds. To this end the questions I'd first ask myself are these. Are my outs clean (are there any bigger straight or flush draws in my opponents range)? Am I willing to stack off unimproved on the flop or turn with outs and fold equity? Most importantly - what is my opponents range, and what is my equity against that range.

Ok, let's assume he has 33, 55, 66 (9 combos) or 77-TT (24 combos). If you bet on the turn will you get any sets to fold or overpairs to call? If he bets on the turn will you call? If you hit your straight on the river is he more likely to pay you off with a set if he bet the turn or if you bet the turn? If you check the turn will he bet his overpairs?

If any made straights or flush or straight draws are in the villain's range I'd fold to the flop raise.

If no made straights or flush or straight draws are in the villain's range I would perhaps:
3bet the flop to $4 or so. Problem is that if I get shoved on by sets only I almost have to call. A call would be slight -EV, but any overpairs or bluffs in his shoving range makes it around 0 EV. I'll calculate with folding as if it's 0 EV the EV comes out the same if we call the shove or fold to it. If his range is exactly as described and he folds his 77-TT range out of 33 times we pay $2.1 33 times ($69.3) and take home $3.5 24 times ($84). So I could 3bet/call and embrace variance, or I could 3bet/fold and avoid variance. But the flop 3bet I think is profitable regardless (assuming this range is remotely correct) on fold equity alone.

Check/fold the turn. The underlying theory here is that no 77-TT hand will feel so good about the turn that they will bet it. Of course, the villain may have the same thought as you, think it a scare card and bet with what he now thinks is the worse hand (you could have a bigger overpair) or a marginal favourite (to a nut flush draw) which he'll be happy to take the fold equity on. Check/fold turn doesn't really work.

Bet/call turn shove. Problem here is that while on the flop we have 27-31% equity based on how we form the shoving range (33,44,66 with or without KK is my reference) on the turn our equity is 20-21% and we have to fold. Bet/call turn shove is bad.

Bet/fold turn. We bet here to fold out the overpairs that are weak. The question is whether we can believably represent the AhXh hand. I guess we could call with it, or as I outlined above - 3bet the flop with it. If he thinks you are the kind to 3bet AhXh then he won't give you credit for it, but will instead give you credit for a bluff and call you down. With a set he may still simply call you to let you hang yourself. So bet/fold turn only becomes a river all-in if you hit your straight outs.

On fold equity alone I think the flop 3bet can be more profitable because you can get away with a smaller bet relative to the pot because people don't understand raise sizing, but with the flop bet/call, turn bet/fold line you may end up seeing your straight complete and extract from sets, which is probably the most profitable line.

Now, examine my post closely and judge all of the assumption regarding the opponent range, try to make some different assumptions and make the corresponding calculations and see where that takes you.