I'm very new to PLO. Just wondering about this hand.

On the flop I thought there was some chance that he was betting a draw, overpair, 2 pair, set. Is that a realistic range?

Poker Stars $0.01/$0.02 Pot Limit Omaha Hi - 9 players
The Official 2+2 Hand Converter Powered By DeucesCracked.com

Hero (BTN): $2.97
SB: $2.63
BB: $1.91
UTG: $1.50
UTG+1: $4.98
UTG+2: $3.33
MP1: $4.82
MP2: $0.72
CO: $5.22

Pre Flop: ($0.03) Hero is BTN with A A T 5
UTG calls $0.02, UTG+1 calls $0.02, 1 fold, MP1 calls $0.02, MP2 calls $0.02, 1 fold, Hero raises to $0.15, 1 fold, BB calls $0.13, 2 folds, MP1 calls $0.13, MP2 calls $0.13

Flop: ($0.65) J 9 3 (4 players)
BB bets $0.65, MP1 folds, MP2 folds, Hero raises to $2.60, BB calls $1.11 all in

Turn: ($4.17) 7 (2 players - 1 is all in)

River: ($4.17) T (2 players - 1 is all in)

Aggression on the button is great, and I don't mind pre flop at all. With these Aces you can hit two straight draws (broadway and wheel), a flush draw, or obviously top set. When you hit those you'll want to get a lot of money in. In addition, you can try to aggressively charge people for drawing if you can get with just two or three people in the hand.

Once the SB leads out full put into 4 people though, his range is narrowed to almost entire top two+ for made hands and strong draws. I don't think an overpair is in his range here. If you're new to Omaha, however, the concept of 'drawing' can be a lot different then hold'em. In Omaha, you could be a dog to his draw. Give him a wrap for example:

board: Js9h3d
Hand Pot equity
AsAhTh5d 42.51%
KQT8 57.49%

In Omaha you really need a hand that you can safely go to the river. Aces simply aren't as strong as a hand in Omaha because one pair by the river is very rarely the best hand.

For your hand, once he leads out, you're a big dog to a reasonable range of hands that he could be leading with:
board: Js9h3d
Hand Pot equity
AsAhTh5d 26.56%
KQT*,JJ**,99**,J9** 73.44%

So just fold.

don't raise this flop ever. call or flat

Easy fold with an overpair and nothing but backdoor draws. The fact that so many micro stakes players will commit their stack in this spot with your hand is precisely why you don't need to. There are plenty of opportunities to get it in good and take their stacks.

I understand the argument for folding. I don't really get the argument for calling. Isn't Folding > Raising > calling? Why would you call?

There can be some good turn cards bricks, the board pairing, heart, etc.

If I call, the pot on the turn is 1.95 and villain will have 1.11 left. Would he honestly fold there very often?