I replied at Stox on this hand, but decided to do a bit more work on it and came up with some interesting numbers.
Calling is out of the question. I hope I don't have to explain why.
If we shove and he folds, it's clearly good for us. But he just made a committing 4-bet and I think a tight reg will know that. He has no intention of folding.
There's 8+33+2 = $43 of dead money in the pot when the action gets back to us, and the stacks are effectively 100BB deep. If we shove and he calls, the money we stand to win is $43 + $200 (his stack) and the money we risk is $167 (the rest of our effective stack).
So we risk $167 to win $243. How often do we need to win to break even?
243:167 = 1.46:1, or about 41%. Actually slightly less, but we don't want to break even, we want to how a profit. So let's go with 41%.
... and now we construct his range:
Equity versus only AA and KK: 18%
Equity versus AA,KK and QQ: 31%
Equity versus AA, KK, QQ and AK: 38%
Equity versus JJ+,AK: 40%
Yeah, this is scary close. The question we're asking here is "is JJ in his range?" and "in that case, is JJ as likely as AA?"
For shits and giggles, a range that includes AQs: 43% to win.
This is where recent history versus this opponent comes in. If we're perceived as reckless, he might be 4-betting AA here hoping that you'll come along with a lot of crap. But if you've been playing somewhat tightly, then wouldn't he flat at least some of the time with aces here?
Then, again, he just made a committing 4-bet. With a very optimistic range, we're showing a profit. With anything but an optimistic range, we're not. So I revise my StoxPoker answer and change it to "fold." But it's close.
In the words of Eric Cartman, it's hella close.
If there's some chance of him tilting or pulling a "iknowthatyouknowthatiknow" outlevelling bluff, it's a snap call.