*grunch*
I can feel your pain with 3betting JJ preflop. I still do it, though. But I never feel too comfortable about it.
Villain caps preflop and 3bets the flop. He might be quite loose preflop. But his stats don't look like he's going overboard postflop. Therefore I'd put him on AA, KK, QQ, AK. That might be a bit too narrow. But without further evidence I wouldn't assume villain to cap with TT, AQ or KQs. Still you are behind most of his probable holdings and the K kills you a lot of times. I think you evaded a check-raise on the river.