KK deep OOP vs. 6max limp-raise

[Cryptorchild]

Villain in this hand limps often and is something like 38/14/2. He's limp-raised me once before in 6max with KK in probably 1 or 2k hands together.

6-max 2/4NL and I'm in the SB with $750 and villain has me covered. Villain open limps the cutoff and I raise to $20 from the SB. The BB calls and then the limper raises to $65. I...?

This is one situation I've never been in before and really had no clue as to what to do. The range I'd put him on is AA, KK, and QQ. But I feel as if QQ is a little less likely. AK is probably a possibility as well but significantly more unlikely than QQ.