Turn re-raise from villian on missed flop

[Joe Taylor]

This situation seems to be coming up quite frequently in my games lately, so I thought I would post and get a feel for how other people are handling it.

Party 2/4. An example hand, but the details sometimes vary. I'll get a hand like AQo, and open-raise from UTG+2. It will fold to Villian (example stats - 22/8/1.9 - it varies a bit), who is in either MP3 or CO, who will cold-call the raise. Button, blinds fold.

Flop comes down KJ3, rainbow. Missed my two overcards, but of course I lead out, villian calls.

Turn comes rag, I lead out again, villian raises.

What's your play?

I've been folding a lot here, but in the times I've been annoyed and called down (when the same person has done it a couple of times), I've seen everything from AK, KQ (reasonable, I suppose) to hands like 88, which just boggles my mind.