Spots like this are exactly why you don't coldcall this hand, but sounds like you already knew that. I would raise the flop. If villian is a TAG, he could easily think you coldcalled with 66, and you could get to showdown or draw to likely five flop outs for cheaper. That being said, many could still not fold JJ, QQ etc. on this board, so hard to say what your FE is without knowing the villian specifically. Given you called, turn fold is easy with likely only 2 outs.