3-bet preflop is fine. Against a 4-bet it depends a lot on how often they 4-bet. Call is fine, 5-bet is fine. Fold seems nitty but if they barely 4-bet it could be fine.

I think it is really very player dependent. A lot of players don't have a very sophisticated 2bet, 4bet game. Hud is important, or reads. How often do they 4bet, do they fold to 3bets, what do they do on the flop? - will they fold to a cbet? A lot of worse players will only commit with AA and KK here.

JJ is a strong hand but also notoriously hard to play postflop so a clear idea of what you are going to do on various flops is important. In this case if you call $2.60 there is $5.30 in the pot and you have $7.40 behind so its a very low SPR. For example, if the flop is low a good Villain will likely have AA, KK, QQ that beat you, but if he is not tight will have hands like A2S-A5s and possibly some KXs (and possibly TT if he 4bets that) which you can jam on.
So it's all a case of thinking what his range is and going from there.

For what it's worth, against an unknown in this spot at our limits, I'd fold. If he's a big bluffer he'll do this a lot and you'll get better spots later because you are usually in position against him.