Hi!
Live 200$ tournament.
Hero open 4000 on 1000/2000 with AKo
V in BB call. (9k pot)
Flop 862rb
V check Hero bet 7000
V shove 14.000. Hero cover.
Is this ever a fold? How much equity do you need to be a profitable call?

You're calling 7k to win 37K, so you need 19 percent equity for a break-even play. Assuming you want an edge since it's a tourney, you need 23 percent or so. (Maybe higher depending on the tourney situation, other stacks, your skill edge, etc.)

At best, you have a 25 percent chance of hitting an A or K on the turn or river. If villain has any 2 pair or set, you're pretty dead.

Considering that he c/r with not much folding equity, I'd doubt he's on a draw or just bluffing. If he led out with a push, I'd be more inclined to think that's a bluff and call. But a c/r that leaves you 4 to 1 is a bet that wants a call, so he's got to have something.

You're getting the right price (barely) against the one-pair hands, and the wrong price against everything better. Although there are way more one-pair hands than better ones, the fact that it's pretty close even just against the one-pair hands makes me want to fold.