JJ on AQx board

[Aves]

Setting is 8 or 9 handed 40/80 at the local casino.

I'm in the SB and probly have a TAG image.
EP+1 is a LAG player who has been raising preflop lots and can get aggressive postflop, but he's not much a factor in this hand.
LP is a NL player who decided to give this game a shot and has been playing a bit loose/passive. He limps a lot in late position first one in and been cold calling lots of raises.

EP+1 raises, LP calls, I 3-bet JdJh in the SB. BB folds, other 2 call.

Flop comes As Qh 3d. I bet, EP+1 folds, LP calls.

Turn comes 7c. I...?

Also, how should my strategy change if the flop and turn had come:

As Qh 3s - 7c

or

As Qh 3s - 7s

Thanks for any replies.