Should I fold JJ in SB?

[LotharOfTheHillPeople]

Hollywood Park Casino Los Angeles CA. 40/80 or 20/40 (can't remember which). WILD player (player A) raises UTG. Two to his left, loose/aggressive/tilting player B 3 bets. Two to his left (assume everyone in between folding), fairly tight player C cold 4 bets. Player C is a bit short stacked due to beats and getting blinded away. The action is on me in the SB and I find JJ. However, before I act, the BB says "I'll cap it". Not sure whether he knew it was already capped or not. Nevertheless, I knew he was in and that wasn't good news since my read on him to this point was that he was a fairly solid player. It pained me to lay down those jacks, but I felt it was the right play. I figured I had to be up against a better pair or at worst an AK holding. The board came 7 high and player B won with 88s. I didn't regret laying down the jacks at the time, but since then it's been on my mind whether that's the right play. I haven't gotten a lot of affirmation from other people I've asked that this was the right play. Any thoughts?