2barrel OESD & get raised on turn

Villain is 26/8/2 over 40 hands. Villains turn and river aggression were up there, but only over 40 hands. I haven't tangled with him yet and I don't have any good notes on him. I just can't make sense of his line. What plays like this? And was 2 barreling stupid here? The flop looked to miss me, so he either thinks I have KK-AA here and will stack off or I have squat and 2 barrel too much. I haven't 2 barreled at this table, but I am aggressive. Do you call with implied odds or fold to turn raise?

PokerStars No-Limit Hold'em, $0.25 BB (5 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

SB ($25.65)
BB ($28.80) VILLAIN
UTG ($45.15)
Hero ($28.15)
Button ($9.70)

Preflop: Hero is MP with Q, 9.
1 fold, Hero raises to $1, 2 folds, BB calls $0.75.

Flop: ($2.10) T, J, 2 (2 players)
BB checks, Hero bets $1.5, BB calls $1.50.

Turn: ($5.10) 3 (2 players)
BB checks, Hero bets $3.5, BB raises to $10, Hero ???

I don't think you have any fold equity here, so shoving is not the better play. I go for calling and trying to hit.

Just check behind on the turn. As played, fold.

Originally Posted by AHiltz

I don't think you have any fold equity here, so shoving is not the better play. I go for calling and trying to hit.

agreed, and i think betting the turn is fine.

How much $$ do I have to make up on the river if I overpay for my turn draw by $2.50 to break even?

Check the turn. The 3 is not really a scare card and if we make the straight we get value on the river. As played fold.