Preflop vs a NL100 reg you should be able to 3bet/5bet AQo BvB profitably as a default. If you're not 3betting AQ, what are you 3betting? He can 4bet you every time and your range is so weak he prints money or you play passively and he can steal light and still print money. You don't ever put pressure on him.
Ah, I missed your raise on the flop. He still doesn't have set because he'd 3bet flop with it most of the time imo, same with strong overpairs, so I still think the river is a value bet.
On the river, it doesn't matter if he folds 90% of the time to your bet, that 10% he calls you get value since you are supposed to have him beat about 99.99% of the time. If you have the second nuts when your opponent never has the nuts, would you not bet because he won't call too often?!
The fact is you are not repping too much so he can find a call with a hand like 6x, 77, 8x, 99, TT, maybe even JJ if he didn't 3bet flop. With QQ+ I think he 3bets flop and stacks off.
The benefit of checking back is getting info on a reg where you are not sure about the value of a bet. However, betting gives you a very aggressive imagine and in his head you look like an aggro monkey and will think you bluff a lot and will never consider you are just aggressive with thin value hands.
It's easier to find hands that call afterwards than in game when you were thinking you are bluffing and all of a sudden you have a good hand, since the bluff was meant to make him fold quite a few hands you now want him to call. Since he would fold a lot of the time, now you get the impression there's no value in betting.