When you 3bet, and opponent 4bets, you can't usually fold. There are some exceptions, but the basic rule is that you can't. If find yourself folding a lot after your 3bet, you are doing something wrong.

Let's say you and villain have 100bb stacks. Villain raises to 4bb, you 3bet to 12bb. Now opponent 4bets to 36bb. You need to pay 24bb preflop, and you have good implied odds. On flop you need pretty much 30% equity to call his shove, and with 9977ds against AAxx range you will hit the flop for at least 30% equity 1 out of 2 times. And when you do, your average equity is about 60%. So you are making tons of money.

You will have to pay 24bb. 50% of times you will fold on flop, and lose that 24bb. Other 50% of times you will get the money in with average equity of 60%. So you will win 38bb more on flop, plus the preflop pot (I have fever, so too tired to calculate the precise EV).

What if opponent has smaller stack? If he has 36bb stack, you just call it. You need to pay 24bb for a 72bb pot, so you'll need 33% equity. With 9977ds you have 41% equity. So with 0 implied odds your basic odds are enough, and when villain has more stack your implied odds get bigger. If you are 100% sure that he has aces, you just call his 4bet. Even if he has something like 5bb's left in his stack. If you can fold to at least 1 flop, it's better in EV than just 5bet shoving 9977ds. If flop comes A22 or AA2 you just fold. And save that 5bb (or whatever).

I don't know if that makes any sense, as I said I have fever so my thought process isn't that clear. I have made some videos about the math behind 3bet/4bet stuff, maybe they will get translated to english at some point. As quite many players have some leaks in understanding the math behind calling 4bets etc.