AQo on the BB in a 3bet pot in a blind battle

Without looking to spoiler: You might want to xb flop. We do have BDSD but in 3-bet pots, I think when we haven't hit from a draw on, we should xb. I am not sure what are villain's tendencies are postflop. I think you can approach this problem with 'how often does villain fold postflop in 3-bet pots'. In addition, now you have bet, you have to give villain credit after the flop since it is a 3-bet pot. We might want to slow down, even now the Ace comes. We can always bet OTR small. There isn't much value that we can get with our hand.

After seeing spoiler: Bummer indeed. Seems that villain can protect its equity, although calling this hand OOP I think it's not a good idea since you lose value when you go postflop with it (the hand shows only relative equity and can decrease much postflop). I think I stay with my advise and slow down OTT.

I think he played it well. TPTK is nice hand HU. Your most likely made hands are almost all big pairs (either in the pocket or spit), and he beats them all. (Sets are perhaps rare - how often do you 3-bet with 44/33 here (or tiny suited connectors)?) Since you know him, he knows you, and probably figured you'd pay off with worse.

Most of the time you'll have the best hand otf, I would consider even a lower bet

Note that OP asks for comments on villain's play...

I think that SB vs BB he should 4bet AKo preflop. As played, flop is fine imo, but i think he could check/shove turn or check/call turn, shove river.