$1 PLO wk two pair in 3bet pot oop turn play

I find these spots tricky. To me it would seem that I am ahead a fair amount, but will rarely have good equity when called, should I jam here.
I would describe villain as a bad LAG, not necessarily a regular, but his stats aren't too horrible. He plays 51/36/3, with a 3bet of 9 over 257 hands. His range to the flop could easily be 100% of hands here against me.
Thoughts? Thanks for your input.

Submitted by : InsideMan

$1 PL Hi 6 max - Omaha Hi - 5 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

Hero SB : $141.70
BB: $83.50
UTG: $100.00
CO: $38.73
BTN: $94.05

Hero posts SB $1.00, BB posts BB $1.00

Pre Flop: pot: $2.00 Hero hasJh

fold, fold, fold, Hero checks, BB raises to $3.00, Hero raises to $9.00, BB calls $6.00

Flop: $18.00, 2 players
Hero bets $12.00, BB calls $12.00

Turn: $42.00, 2 players
Hero

He plays waaay too many hands for this not to be a bet/call, especially with those stack sizes. I would just bet something like $32 and not think too much about it.

Are we doing the same with naked AA here?

^ yes, check-folding sucks, I think even a good jack is enough to bet/call here. There's a ton of pair+draw combos that he looks you up with. If he's really laggy we can discount sets, 2pair, a straight a lot cuz he didn't raise flop.

@ NMcNasty

Thanks for your input.