I was faced with a similar situaton late in a MTT recently, though I had the other half of the coinflip. AKo, PF raise to 4x blinds. Slightly smaller stack who had been trying to buy a lot of blinds goes all in. I put him on 99-QQ, slight chance of KK or AA, AJ+, with a better than average chance of a bluff since he'd been caught bluffing big at pots a few times. I made the call for most of my stack getting about 2:1, knowing that a win would make me a big stack and significantly increase my odds of going deep as opposed to just finishing in the money.

He had jacks. I made a straight to ace. He made quad jacks. Fun game, this poker.

I'd call here too. It's worth it to build up the monster stack, especially in your case where you're on the slightly plus side of the coinflip.