200NL
Villain on btn has been loose aggro so far, but only one hand showed down, where he got KK in vs TPTK and doubled up.

Villain BTN $4 (2bb)
Hero BB 87o calls

Flop ($9) AA7r
Check x2

Turn ($9) AA7A
hero bets $7, Villain calls

River ($23) AA7A2
Hero checks
Villain bets $31
Hero calls.

Here I expect a lot of medium pairs and Ax to bet, so didn't make a lot of sense to face an over bet here, but I think it's a very under bluffed line with this sizing. Not sure if this is a profitable call or not, but don't think I can fold either. Also should I be bet folding this river? Target some 22-66 hands, if so which sizing?