This type of spot comes up a ton in tournaments, so good topic for discussion. Two main thoughts.

First of all, as played. You cannot fold here. I would estimate that 98% of the time (I know this sounds silly but I really think it's in that neighborhood!) your hand is no worse than 45% here (vs QQ, JJ, etc). Granted some players will have some of your As and Ks, reducing your equity, you still have more than enough with dead money in the pot to compensate and make your pot odds worth it. You're going to be flipping vs two pairs pretty often. It's not out of the question to think that the initial flat caller could shove with hands we dominate (as the results show!).

Secondly, what do we do when the SS first shoves? Do we call or reraise at this decision point? My initial thought was that we should reshove, attempting to encourage folds from pairs that we're doing okay against equity wise (it's 50/50ish), but would rather see fold and not have to face their 50% equity in the pot. Upon further consideration, we should call here, as you did. The reasons are we will dominate so many hands that the early position players will continue with. I would mostly expect flat calls from these players with hands like KJs and AJs. But, as we see here, some players are more frisky than others, and could end up jamming with marginal hands that we dominate. I would also expect players to not be as willing to fold JJ or TT if we did indeed shoving, reducing the benefit we're aiming for with making that play. If you have any reason to believe that players are capable of what we see here, then you need to trap with your hand. It may not seem natural to trap with AK, because it may not seem strong enough. But just as AA dominates QQ, AK dominates hands as well. Thought admittedly the dominating isn't as strong with AK vs other Ax or Kx, from a sheer equity standpoint. Conceptually though, we need to realize these situations are the same. 

I'm not sure what tournamnt this is, but what I'm taking away from this is that this is an important reminder to remember who we're playing against. If it's a smaller buyin or perhaps a turbo, players are going to be more apt to take chances, or more apt to simple make poor plays. Because of that, every good hand goes up in value, relative to what they have.