NL10 JJ facing squeeze

[converted_hand][hand_history]PokerStars - C$0.10 NL (6 max) - Holdem - 6 players
Hand converted by Holdem Manager 3

SB: CA$11.24 (112.4 bb)
BB: CA$7.82 (78.2 bb)
Hero (UTG): CA$18.79 (187.9 bb)
MP: CA$16.65 (166.5 bb)
CO: CA$9.74 (97.4 bb)
BTN: CA$10.00 (100 bb)

SB posts CA$0.05, BB posts CA$0.10

Pre Flop: (pot: CA$0.15) Hero has J♣ J♥
Hero raises to CA$0.25, fold, CO calls CA$0.25, BTN calls CA$0.25, SB raises to CA$1.35, fold, Hero?
[/hand_history][/converted_hand]

CO and BTN are both weak recs. Against most of the pool I would think the squeeze here is very value heavy, but the SB has been fairly aggressive preflop (PFR 24%, 3B 13% over ~350 hands) and I expect they will be fairly wide here knowing the CO + BTN will have a lot of folds.
I think they're squeezing range likely looks something like this:

I don't mind calling against this range in position, but I think if I flat here one or both of the CO + BU are likely to call as well and I think it's difficult to realize my equity post flop with this hand multiway. I decided that I liked a 4 bet here. I think vs a 4 bet the CO + BU have basically zero calls and I can put the SB in a tough spot with large portion of his range. I ended up going with a jam, I think this gets a ton of folds from hands with reasonable equity against me and even potentially some better hands. They will obviously call AA, KK and AK. I expect AQ is probably mixed, and I think we actually get some folds from QQ here given how tight most of this pool is pre. I expect everything else is a pure fold, denying villian a lot of equity and also avoiding paying the insane micros rake.

Curious on everyone's thoughts on my thought process here, and how they would play this spot.