I get cr'd on turn and push a big draw

[Big Poppa Smurf]

Villains like looks weird, and in retrospect, it does kind of look like a big hand. At the time I felt the stacks were deep enough to give me some fold equity if he has something like AA, and obviously I have a lot of outs against most of his range(barring KT, which seemed unlikely). However looking back at the hand I think I really overestimated my FE here.

Should I even be betting this turn? If so, is my bet size ok or should it be smaller, like 4-5?

Party Poker No-Limit Hold'em, $ BB (5 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

BB ($21.65)
UTG ($23.05)
MP ($38.98)
Hero ($36.25)
SB ($52.47)

Preflop: Hero is Button with T[img]/images/graemlins/heart.gif[/img], 9[img]/images/graemlins/heart.gif[/img]. SB posts a blind of $0.10.
<font color="#666666">1 fold</font>, <font color="#CC3333">MP raises to $1</font>, Hero calls $1, <font color="#666666">1 fold</font>, BB calls $0.75.

Flop: ($3.10) 4[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/heart.gif[/img], 9[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, <font color="#CC3333">MP bets $1</font>, <font color="#CC3333">Hero raises to $3.5</font>, BB folds, MP calls $2.50.

Turn: ($10.10) J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
MP checks, <font color="#CC3333">Hero bets $7</font>, <font color="#CC3333">MP raises to $19</font>, Hero calls $24.75 (All-In),