Online I would typically just jam it in and live with the outcome, unless its right on the bubble or something. But then I would typically not be 60BB deep, and if I was, I would probably not 3-bet in the first place. But I assume, this was a live tournament, and then this spot frankly suck, because what is a tight low stakes live player realistically 4-betting with here for 1/3 of his stack out of position?
Even if he has something as strong as AK or JJ-QQ, I think, he is more likely to just call our 3-bet and see a flop. So I think, we are against KK or AA here a lot, which mean, that 5-bet jamming will obviously be a complete disaster. I also dont like calling, because then there will be 40BB in the pot and only 40BB left behind in our stack, and mostly we will just be delaying a difficult decision to the flop.
On the other hand if we fold, we still have 52BB left, which is an absolutely workable stack especially in a soft live game. So I him and hum a bit, and then I fold without showing. I absolutely do not want the table to know, I folded a hand as strong as AKs. I want people to believe, I was 3-betting light with a hand like A5s or KJo and had to let it go facing a 4-bet.