JJ - SB

If you don’t cbet this flop you will most likely lose the hand for sure, because he will never check it down until the river. It’s indeed right you get only action of better and I don’t think check/folding isn’t too bad on a wet board like this.

Cheers,
SDK1987

Make it bigger preflop so you don't give him good pot odds. (Important: Being OOP you want make bigger 3bets as you don't want play postflop that much acting first on every street, IP (being btn especially) you can make smaller 3bets as you will be in lot better spot postflop acting last on every street deciding how much money goes in pot lot better)
3-3.5x his open (8-9bb 3bet), putting him into spot where he need decide more between 4bet/fold more often.
Postflop check/call once seem fine, he can sometimes bet weaker draw/weaker pair and check down.
Would not hate check/fold flop if you believe player is capable betting multiple streets his draws.

With two overcards I don't think that calling is correct.
I mean, he called a 3 bet. It's very likely that he has an ace or a queen.

Only hands you beat are flush draws and if you call the flop you need to call on the blank turn as well.

Why are you all assuming his 3bet is good? We're playing 55bb effective and this dudes who apparently is a regular raised from UTG. There's loads of discussion here about a spot in which we shouldn't be in. What if the reg 4bets us, are we really getting in 50bb vs an utg raiser happily? Don't think so. Are we 3bet folding then? JJ is a bit too strong for that. Call preflop, see a flop and go from there. We're not only setmining here, there's loads of good flops where you can easily play checkcall, checkcheck and vbet river.