Hand quiz: Tough JJ overpair hand four-way

Is tough JJ hand redundant?

I thought this was an interesting away-from-the-table analysis problem that would help everyone make a better decision in this marginal situation.

CO is 54/19/1.7 and does not 3-bet lightly; other two are VPIP > 30-40, fairly passive.

PokerStars 1/2 Hold'em (6 handed) FTR converter on zerodivide.cx

Preflop: Hero is MP with J[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/spade.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises</font>, CO calls, <font color="#CC3333">Button 3-bets</font>, <font color="#666666">1 fold</font>, BB calls, <font color="#CC3333">Hero caps</font>, CO calls, Button calls, BB calls.

Flop: (16.50 SB) 5[img]/images/graemlins/club.gif[/img], 4[img]/images/graemlins/spade.gif[/img], 3[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(4 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, <font color="#CC3333">CO raises</font>, <font color="#CC3333">Button 3-bets</font>, BB calls, Hero calls, <font color="#CC3333">CO caps</font>, Button calls, BB calls, Hero calls.

Turn: (15.25 BB) A[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(4 players)</font>
BB checks, Hero checks, <font color="#CC3333">CO bets $1.25 (All-In)</font>, <font color="#CC3333">Button raises</font>, BB calls, Hero?

What is your line here and why?