I would have raised 4x BB preflop.
Everybody would then probably fold, if SB still had called you could have put him on a hand post-flop.

He probably flopped middle or top pair with the 3 kicker wich came of the turn or maybe J9.
If you had raised preflop and he let's you know that he has a good hand (A3 of J9 would have been folded after that raise) by calling your flop bet and after that betting the flop you get out.

I think he checked the flop with 2 pair because he's afraid you'll fold if he bet, after he called and the 3 comes of the turn he bets because he does not want you to draw to a possible backdoor flush.

Anyway, i think you played the hand pretty bad.
If you decide not to raise preflop, than bet the pot on the flop, don't save that 20 chips.
After he bets that little amount on the turn in comparison to the potsize, raise him (and not the minimal raise).
If he calls and checks to you at the river, check it also.
If he comes over the top, drop your hand.
But don't just call his bets!

Some people want to avoid this kind of situations early in the STT, if so, fold preflop, easy enough.
I don't mind playing these type of hands early, but if i feel my hand is weak or my opponent is stronger, i fold.

That's how I think about it, i'm curious to read more ideas about this hand.