AK is commonly overplayed. Also most players have a tendency to say “I put you on Ace-King” to any 3better. Not only is AK a speculative drawing hand, but when you do make something it’s very obvious to your opponents. Preflop the value in AK for me is more about the card removal. Blocking AA and KK is a huge piece of information that should give you confidence to 3bet with.
But why I dislike your flat is less about your cards and more about the lack of clarity in this scenario. You were setting yourself up to play against at least 2 and potentially 4 opponents from the worst possible position. If the limpers called (and I’m actually surprised they didn’t given their pot odds) they can have almost any two cards. If an ace or king does come on the flop you have no idea where you are. You’re either going to be so far ahead that you can’t value or more likely behind against multiple very wide ranges. Further being this far out of position gives you little ability to control the pot size, which means when you are behind you’ll lose more.
A large 3bet would narrow the field of opponents and significantly narrow the range of anyone who called you. As played, unless someone was trapping, I’m the only one who can have a premium hand but this is unlikely given my loose image and high opening frequency. With your blockers and the respect an astute player should give to an SB 3bet, such a raise would have a high probability of getting folded around.
If you disliked 3betting, folding is a better option. It would be exceptionally nitty but you would ultimately be choosing to risk zero chips holding ace high. There aren’t many scenarios where profit can be extracted, and many where you can lose a lot.
As an even more absurd alternative, I would even consider a 3bet shove. But flatting is absolutely terrible for more reasons that I can type out in one sitting.
