3/6 JJ+rags - maximinize winlosses

[AllIn3High]

3/6nl on UB. 6 handed.

Preflop:

56/19/2.5 LAGgamuffin [Villian, $675] limps UTG+1 (this means he has something remotely playable that isn't good enough to raise).

Folded to me [$632] in the SB; I raise pot with J[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/diamond.gif[/img].

Bad chasing donkeymonkey [$549] BB calls,
Villian calls.

Flop: 6[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/club.gif[/img] (Pot $72, 3 players)

I bet the pot, BB misclicks and folds, Villian calls.

Turn: 6[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/club.gif[/img] - 6[img]/images/graemlins/spade.gif[/img] (Pot $216, 2 players)

What's my line? How do I maximize my winnings and minimize my losses? He's bad but not exceptionally bad, he can fold and he can make decent bluffs.

I'm not worried about him having an overpair here, but he could have a set, medium pocket pair, 5x, 6x, gutshot, overcards.... I'm not sure how often he will bet a worse hand/bluff/draw if I check to him, or how often he will come over the top with a worse hand, he's pretty aggro.

All comments appriciated.