To weak with JJ as an overpair?

I would have bet the flop to at least $2.50 and potted the flop. If he is willing to come over the top of that... then it is definitely time to re-evaluate, but you raised from the blinds (sign of strength), raised big (sign), bet the flop hard(sign). As played... your plays seems exactly like "I have this great hand on the flop, JJ/QQ, but [censored], that K scares me, please don't bet too hard."

The problem is... I'm not sure what size bet to make because of his short stack. If you bet half-pot after a check-raise like that, you're betting the same amount and that still telegraphs weakness, but if you bet more, he won't really have enough behind to make you fold if he comes over the top. As played... I would have bet $15-20 (2/3ish), and depending on my read... called a reraise but hoped for a fold. To 4_2_it, what line do you suggest?

As it stands... the 3-bet on the flop really bloatted the pot, but that was the right play. I think the easier way to avoid this problem on the turn or river is to bet hard pre-flop and pot the flop. Make him define his hand sooner.