It seems to me that it could easily be profitable to call the 3.5xbb raise if you know without a doubt that he has AA or KK, and of course that he does not know that you have this perfect read on him.

If an A comes on the flop, bet anything less than a pot sized bet and 50% of the time he will fold his kings if he's a good player. Meaning, you are getting better than 1:1 pot odds. If he calls or raises get out ASAP because it means he's got trip Aces.

Similar thing can be applied in the case of a K on the flop.

If neither A or K on the flop, you may be able to man handle him pretending to flop trips, a straight, or whatever the board scares up. It's a game of information. If you have perfect information on what he's holding, what more can you ask for?