50NL - JJ on a low-card board

[thing85]

This villain is 28/15/1.5 over 60 hands. No other reads on him.

Poker Stars, $0.25/$0.50 NL Hold'em Cash Game, 6 Players
LegoPoker Hand History Converter

SB: $54.80
Hero (BB): $56.85
UTG: $34.55
MP: $3.55
CO: $22.75
BTN: $65.70

Pre-Flop: J[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/heart.gif[/img] dealt to Hero (BB)
2 folds, CO calls $0.50, <font color="red">BTN raises to $2.50</font>, SB folds, <font color="red">Hero raises to $8</font>, CO folds, BTN calls $5.50

Flop: ($16.75) 2[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/spade.gif[/img] (2 Players)
<font color="red">Hero bets $12</font>, BTN calls $12

Turn: ($40.75) 4[img]/images/graemlins/diamond.gif[/img] (2 Players)
Hero...?


I put villain on overcards or a small/medium PP. Since it's unlikely for him to have a draw and he called my large flop bet, what's my play on the turn? Do I push hoping he'll call with lesser PPs? Check to induce a bet? I only have ~$36 behind, so any bet I make is going to wind up putting me all-in at some point...