Villain is reg on the $7 stakes. Iso would be 27%, and c/r very low 1 time out of 38.

PokerStars - 10/20 NL (2 max) - Holdem - 2 players
Hand converted by PokerTracker 4

BB: 19.5 BB
Hero (SB): 30.5 BB

Hero posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has J 5

Hero calls 0.5 BB, BB checks

Flop: (2 BB, 2 players) 3 J 8
BB checks, Hero bets 1 BB, BB raises to 3 BB, Hero calls 2 BB

Turn: (8 BB, 2 players) 2
BB bets 5 BB and 10bb behind, Hero?

I would start with a check back otf. As it is hard to get three streets of value.

When you get raised, you are in a tough spot, as this is not the top of your range.

And then you want to protect your checking range, too.

Kinda meh spot.
If you really think this guy is superstrong when check raising, than you have to fold on the flop. If he is really tight passive than just bet/fold flop, if you think he can have wider range, than calling flop and this turn but by wider I dont mean he also can have draws, even if he xraise some good draws thats not enough to call this. But looking at stats you provided id prob just bet/fold flop.
@Vvvvv
while in theory we should check here a lot but we have reads villain is not xraising and we should take advantage of it by betting a lot here. Same goes for most betting spots, how wide and thin you want to bet depends on how much you will get raised.

I would bet all my Jacks on the flop, there is too many draws out there that pay 1bb and our hand is vulnerable vs overcards. Vs XR im calling flop and possibly turn vs anyone, even if his xraising rarely he could still have a strong flashdraw and decide to play so. In the most common scenario you are versus a better Jack or two pair you have outs most of the time (unless he has exactly J8). When you hit your 5 its very likely to win your opponent stack.

Are you BB or SB?

Assuming Hero is SB as it says, then I like the flop bet and call.

The 5bb turn bet by BB (assuming SB checks) looks like a better J or a bigger hand. I would probably fold. If villain bluffs a lot, I might call.