AA 3 barrell vs fish

I think this play might be decent against a player that plays like that. But I think one big problem in this hand is that you assume your villain is loose aggressive fish just based on 113 hands. I have demonstrated how big a sample we need in one of my videos, and this 100 hands is not enough to get even realistic VPIP/PRF.

So, after 200 more hands his VPIP/PFR can really be 30/25 or something like that.
In this hand sample fold to 3bet,aggression and fold to cbet stats are pretty much useless also.
WTSD is totally useless.

I think he would probably raise a set by the turn, but then the Q on the river would worry me. It’s quite possible that he defended QQ preflop and check-called it twice. Maybe it’s a nitty play, but I’d check behind OTR. Then again, I guess he would bet out there if he had QQ, so perhaps AA is still ahead here; he could play AK this way, I guess. But does he call a bet of more than pot size with JJ or worse?

Be careful with just discarding small samples, or giving them too much weight
There's a chapter in mathematics of poker on Bayesian inference
I looked at the math, but haven't precisely broken it down in a ton of practical spots to be honest but intuitively pretty much everyone uses it
But basically you have a hypothesis ( loose and aggressive fish)
And any piece of incomplete information increases the likelihood of that being the case in a significant way, the more precise the higher the probability.

The correct approach will probably somewhere in-between the two ends of the spectrum of
"He's XYZ"
And
"the stats are pretty much useless"

If you combine stats with actual hands he showed and lines he took at the table you can start profiling players really fast when you combine those, it's like putting together pieces of the puzzle, the more you got and the bigger the connected areas the more you can be sure of what's in the picture even though you'll never see the whole of it until you connect every single piece

I do not get the question. You are asking if you should 3b AA preflop or you are asking if betting on 3 streets postflop is ok?