Second Pair bet on turn bad ?

I think OTT you could also check back as villain would most probably barrel with flush draws and most top pair kind of hands, I think by doing this you allow villain to bluff on the river, also you could even bet turn and river going for some thin value as you block some backdoor flush combos

Agree with cms. I'd check back turn often. You're building a bigger pot by betting, board just got drawy, he could try some weird move and you just wouldn't know where you stand.
I think this is not the best board to float. Sure, villain may cbet a lot and then give up and it would make sense, but not with JJ.

I would just SQZ preflop with JJ - I can take pot preflop or I most of the time I will play vs 1 villain IP
As played I would chb turn as villain Cbets in 3 way pot so he should be stronger than Cbet 1 vs 1. Maybe this is very weak but I think we could fold this OTF as we dont have outs to improve ( only one out - Jd) and board is villain can continue a lot on turn

I like squeezing here preflop. As played, I like the turn bet. First, it would give us free showdown on the river and we would charge his Ax type of hands that got a gutter. Backdoor flush draws will also call.