I really don't like folding here. Think about the standard player's 2-bet range, it's pretty wide, right? Especially at 6-max, suited connectors, suited aces, broadway combos, just about any pocket pair, etc. Now, think about a standard player's 3-bet range, some suited broadway aces, bigger pocket pairs, some offsuit big broadway aces. We're behind to AA and KK only, his range includes far more than AA and KK. If you only play the villain's stats, and in this case not even a deep sample, then you run the risk of not getting enough money.
Personally, I like four-betting here, our four-bet range should be very narrow, QQ+, AKs and will let villain know we're serious. If he has a hand that holds up against our range, he will let us know.
Hell, you don't even have to four-bet big, you can disguise it as a value bet, trying to build the pot as much as you can. What's the worst case scenario? He goes all-in and we fold? It's better than folding against his very wide range, most of which we're beating.
If he was holding AA or KK, which I doubt he was, you definitely lost the least amount of money possible.