NL4 - folding AA after committing half of stack

If its vs a fish there's no way you can fold that turn after betting imo, he can easily have a J that now just ships it in because he thinks its less likely you have a K, or indeed QQ, and you will also see random stuff like TQ, 89d there some of the time. The odds you give yourself by betting turn that big are just so good you really can't fold.

Yeah it made me feel bad to fold that after how much I threw in. I was thinking at the time he wouldn't be THAT stupid to call a 3bet preflop and a big cbet OOP with something that's weak/drawing.

A better line could've been to check the turn and use the AA as a bluff catcher on the river. If not, a half-pot bet, giving me better fold equity at least.

3bet bigger! you are giving the original raiser good set mining odds with that sizing. i'd pick something like 10 big blinds.

as for postflop, i agree with the other poster.
if you don't want to commit yourself you should pick smaller betsizings - which you usually should be doing in a 3bet pot anyway since you don't need to be betting very big to get all the money in by the river.

on the turn it indeed sucks to be raised, but you just commited yourself with your bet. let's go into some maths:
you need to call $1.43 into what is going to be a $2.58 + $3.36 + $3.36 = $9.30. that means you need 143/930 = ~15.4% equity for a call.

i'd expect to see a K most of the time but we should be priced in for the few times he's raising a J or a random draw, which a fish could do because he just feels that he would be commited by calling anyway.

now about turn lines... it's tough to say what is the most optimal line, i think that a small bet is best but turn stack sizes are very awkward due to your huge flop bet.
so my betting plan would be ~$0.60 on the flop (enough protection in a 3bet pot), then halfpot on the turn and shove the river. with that sizing plan we give ourselves room for folding such specific bad turncards.

Checking the turn and bluff catching is definately an option, and if he makes some kind of weak blocker bet on the river you can raise for value.

You do lose a bunch of value vs hands like AJ, QQ, QJ, JT XdXd and AQ/QT/9T if you don't bet the turn but ofc a lot depends on how many of those hands are even in his preflop range, which given he (cold!) called a 3bet they might not be - so your reads/stats on him in that respect are very important.