AQ PF hit Two Pair OTF

Preflop I would just flat the 3bet. Both his 3bet size and your 4bet size are strange.

I see no reason to slowplay flop in this situation. Both of you have tons of Ax and he will call at least a flop be often. I believe a small bet should do it.

Turn is interesting. You have some missed flushdraws (76s, 87s) with no showdown value that should be betting. Your Ax's (including the flush-draw) should bet the flop, so I think that flat calling is better than raising the turn as played. The probe bet should be a mix of bluffs and made hands, but with that size it is way more value.
River he decides to polarize his range and I think villain played this hand decently. You showed weakness OTF and he believes he has some fold equity.
The only thing that doesn't make sense is the bet sizing. He should bet turn and river big, in order to shove the river and polarize his range to the maximum.
But he has about 100bb left on a 44bb pot OTR and bets pot... I believe he revealed the strength of his hand by betting this way.

You're at the very top of your range and this is not a fold for sure when villain clearly has bluffs (or in almost any given scenario).
I can't also see many hands that beat us here (slowplayed AA, QQ). He should not have 99. He can definitely have AK or even AQ (less likely).
I believe his range consists mostly of missed draws (T9s, 98s, 87s, 76s). That said, I wouldn't expected to get called by worse when we shove river.
Besides, a river shove looks very weird after all that action. The thing is that you're not supposed to have a monster as played and if I were villain I would not expect to be raised at all when I'm polarizing it.

I wouldnt 4bet, as we dont have a good enough hand for that.
I would raise OTF and Turn.

Usually a huge bet OTR means a strong hand, however, as played, i would call. you showed weekness and villain could be trying to take the hand with a pair or something like that.

Preflop call his 3bet, and if you want to 4bet then use 2,5x size of his 3bet. While it's strange I would 4bet around 25-28bb
OTF I cbet approx 2/3 -3/4 of the pot.
As played I only call turn and river.

It is call or 3bet bluff vs aggro villiains, imo.
OTF bet 1/3, he have hand to call.
OTT raise... and OTR too. I would go broke...Cooler...

I seem to make a lot of money by slow playing. Thus, I like your Flop check. I also like the Turn call because you may be successfully slow playing him into a Trap. You got the large River bet that you wanted with no flush possibility. Two Pair is an obvious All-In quality hand. I would have All-In Raised the River. I have admitted that I am a passive limp/call Preflop player. But, I always play my All-In hands aggressively. It does not bother me if my opponent beats my All-In hand with a better All-In hand. That happens in poker. Don’t let that bother you. My average all in poker tracker equity is 60%. I will swing for the fences whenever it is appropriate. “Swing for the fences.” Do non-Americans understand that phrase?