Villain is 45/9/35% in 71 hands. He has 3betted 4 times from the blinds in 28 occasions(14%).
Hero is 24/22/36% in 86 hands.
Reads on Villain:
-He 3bets AQo IP with a min3bet($3.75 after a $1.75 open), he cbets $2 into $7 in a 569tt(not holding the suit!) and stacking-off after a raise from his villain(50bbs). So he doesnt fold!.

Full Tilt No-Limit Hold'em, $0.50 BB (6 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

MP ($111.20)
Hero (CO) ($50.45)
Button ($40.35)
SB ($60)
Villain (BB) ($49.40)
UTG ($19.50)

Preflop: Hero is CO with 4, A
2 folds, Hero bets $1.50, 2 folds, Villain raises to $4, Hero calls $2.50

Flop: ($8.25) 3, 8, 2 (2 players)
Villain bets $5, Hero ?

So we were 100BBs deep preflop. he has 3betted me 3 times of the 4.
Probably is a fold preflop but-
What do you think is the better line here? (the plus EV)
-Shoving right here.
-Calling, then shoving any turn.
-just calling him down.

Any suggestions is appreciated. Thanks in advance.

Well you're ahead of pretty much everything so shipping can't be bad. In a single raised pot I'd consider flatting. The reason I like shipping is because we're in a 3 bet pot so if the turn blanks we may not get the odds to see the river.

I like calling because a villain like this will pay us off when we hit, and we only have to pay the minimum, but obv if villain gets scared of flush cards or overcards but I'd ship now.

im raising this all day

gut shot, over card, flush draw... if there's not a better time to ship it against someone that will not fold (i bet this is the one time he folds ldo), i don't see where.

You are a 60% chance to hit at least a pair of aces if my calc are correct

definitely raising this