[DMBFan23]

I would virtually always call down the AQ, barring further improvement.

I am way more likely to 3-bet the AA, as I have more outs if indeed I am behind. I like to 3 bet the turn instead of the river, that way I get the bets from a semibluff now, and I get the same amount of bets in versus the made hands that I beat, assuming no one improves, with either line.

one reason to wait till the river would be to discourage river follow throughs after his turn raises if he WAS semibluffing, but I'mm calling down AQ/KQ, and I check behind hands like AK on the turn here anyway so I am not worried I am folding an unpaired hand that also may have showdown value. I'd rather discourage the turn semibluff or the turn weak-pair checkraise by 3-betting him right then, as that gains me more IMO by letting me bet for protection on the turn more relentlessly, as opposed to the benefits of a couple more free showdowns in the event I do decide to call down his turn checkraises. Percentage-wise, I fold to so many of them (I check behind the turn quite a bit where bet-call might be more appropriate) that I'd rather they happen less, as opposed to saving a bet here and there when they do happen. perhaps if I had a looser table image, I'd be better off waiting till the river more (especially since I could represent more river cards, and my call of the checkraise wouldn't narrow my range as much as it does for me currently).

of course you mentioned one merit of raising the river, and that is the vastly increased likelihood that a 3-bet is a legit hand. (SpicyF has a GREAT post on this in the archives, it's called something like 'the concept of checkraising to save bets') however, I think that capping the turn out of position will carry that same sanity-check with it, in that it will allow you to at least fold the river UI against a sane oppoennt. against an opponent who will do that with worse hands, you also lose the benefit of the river-3 bet sanity check, and would have to make the wait-to-the-river play for another reason (the metagame considerations I mentioned perhaps).

I like to mix it up with the AA as well, calling down sometimes, 3 betting sometimes. really that's dependant on how I've been playing lately, i.e. if I've been following through a lot on the turn, and especially if I've been folding to aggression, I'm more likely to punish what could easily be someone playing back. if I've been in line, then I'm more likely to just call it down.