He's loose aggressive and he likes to 3bet, i know the sample isn't big enough, but it's still some sort of indication.
What kind of? The sample clearly is basically 0 information. Why didn't you then take into account AF, you said he is aggressive but from AF then he is passive.
So let's assume that he's a good player and only raises 22+ AT+ and KJ+ from MP. He should fold all PPs smaller then TT, he should also fold AT, AJ, AQ and KQ and that's 75% of his range. He will probablly call with TT and JJ and raise QQ+ and AK. Against TT, JJ, QQ and AK I have a coin flip and i'm dominated by AA na KK. Even if he really only 4bets with AK and QQ+ I still have 42% equity against a push.
Do you understand that your calculations and assumptions are just waste here? You never-ever know if he is going to do that. I would say way the opposite here.
Also if you are telling that he folds practically every crappy hand, then why do you 3bet in first place? You should be 3betting when you also assuming that you getting called from worse as AT/AJ/AQ. Otherwise doesn't make sense to 3bet if you just get called by that range what has you beat. Instead just call and keep his range wide.
But since he's loose i expect him to fold less and 4-bet with more. So I would definitely push against a 4 bet even though i will be dominated a few times. Sometimes he might even go allin with AQ.
Why should he go all-in with AQ from MP vs SB 3betting range? 4betting and going broke here vs unknown MP is just -EV in long run and you wont earn profit with it. Clearly overvaluing your AK. Would you EVER go all-in with AQ vs unknown SB? I highly doubt.
So the reasons for making the 3-bet are: taking initiative, taking the pot down before the flop, geting more information about the strenght of his hand, trying to build the pot with a strong hand, I don't mind going all in against a LAG in MP with my equity, if he calls the 3-bet I can stack him when i hit the flop.
Taking initiative
-> and what you going to do with that if your main plan was to make worse Ax hands to fold.
Taking the pot down before the flop
-> why would you want to do that? We might even extract tons of more value from his weaker Kx/Ax hands postflop and especially if we hit big.
Getting more information of his hand
-> how you getting more information? If he 4bets you he has a nutted range but at the same time he could as well trap you and just call with strong hands.
I don't mind going all in against a LAG in MP with my equity
->
How the heck do you know he is a LAG? You clearly have even more information here than Farma does.
And a reason that you are OOP isn't just a reason to 3bet cause you are weak playing hands OOP. So every hand you don't know what to do you 3bet?