I'd say call the 4bet. If he's got a hand worth 4betting he'll be c-betting 100% of the time. Either there's an ace on the flop and you can believe him and toss the KK, or there's no ace and you can shove over his c-bet and pray they're not Aces. I really don't see any way to avoid getting it all in sans an A on the flop.

It's also $2, so you never know what he's willing to push with. The stats suggest he isn't going to push with crap, but he could have just been card dead for the last 83 hands (we've all been there, it's not that uncommon). If he's card dead for 83 hands and watches two Queens slide into his pocket, he may be ready to push it all in regardless of what others do.