Could I have made exploitative fold?

Game is 5/5 580 effective stacks.

Hero in BB with 56offsuit.

UTG+1 RFI $15, 3 callers in middle position, I complete in BB. (Pre-flop police are stupid if they come after me for this one)

$75 in pot to a flop of 5d6cJd. UTG+1 c-bets $20, folds to BTN who calls. Hero raises to $120. UTG+1 tank jams for ~480. BTN folds.

Context: this villain is nitty pre flop, but I’ve seen him make some weird plays post. Also I have seen him stack off with overpairs.

(I think villain has a lot of overpairs that play this way and JJ obviously. In hindsight I don’t think he’s ever jamming here with a draw. But at the time I gave his range overpairs, broadway flush draws. AJ, and JJs. I don’t know what percentage of time he jams JJ here. I’m also at the top of my range here. 55, 66, 56 are all roughly equivalent. )

I call pretty quickly and villain shows JJ.

Could I have gotten away cuz of the 4x 3bet jam or am I just always losing my money to JJ here?