Preflop
There is some argument for just flatting AKo preflop against an UTG open. But there is also value in driving out the players behind you, especially when he only min-raise, which is very small for this stack depth. So I am totally fine with 3-betting here, and sizing looks good.
Now however he 4-bet, and this just suck. When I played 5-16NL cash games back in the day, I learned the hard way, that for a lot of nitty regulars in these games a 4-betting range especially from early position is often pretty much only AA and KK. And of course this mean, that if we have AK, we will get 4-bet less often, because we have the blockers, but when we get 4-bet, we are still against it a huge percentage of the time.
Its different, if we have sort of standard tournament stacks here like 30-40BB, because then the 4-bet is a jam, the range is wider, and we just call it off, even though we are not totally loving it. But we are chopping with another AK or flipping with TT-QQ or even beating AQ or AXs often enough to justify getting it in.
Here however you are 60BB deep, and especially when he only min-raised, this is very close to a 100BB cash game, where the open size would typically be 3BB. You also cant really call here, because you will be committing 1/3 of your stack, and what then is the plan, if you miss the flop? If you are folding on all flops without an A or K on them, its better to just fold now.
So if you continue here, it should be with a 5-bet jam, but the best play is to just fold, unless the opponent is a LAG or maniac. I know, its a really tough fold to make in real time, so I dont blame you for calling, but this is a spot, where you can gain an edge by learning to make a tough but correct fold.
Flop
You hit the K, and he move all-in. There are 6 combos of AK, while there are only 4 combos of KK-AA, and you are getting 2:1. That means, that if this is his range, you are priced in to call it off, even you are only calling for a chopper. The whole reason to call preflop has to be, that you think, you are not only against a range of KK-AA, so as played this is a call, and unfortunately this time it was not a chop.