I think JJ is a reasonable holding for him, but I also think he was dumb (a) for folding it, and (b) telling you what he had.
I suppose it depends on your table image, but only a boring straightforward (or weak) player would push with a King. Why not simply flat-call and pounce on the turn? I'd read a push right there as being a sooted Ace-rag or a baby pair (which would explain your limp-and-call).