How freaking wide is your SB flatting range to a 3x open from MP that you play K7s?

I'd play 97s before K7s. MP opens are expected to be heavily laden with broadway cards and PP's. Having a K with a weak kicker is going to put you in terrible decision spots. Playing SC's for 2-pair+ hands is much safer when OOP against a predictable opponent.

I think the only 3X hands in SB range would be { 33, A3s }. There's plenty of SC's and AXs in a SB flatting range, though.

I'd perceive your range as mostly flushes, sets and Aces up, with an occasional wheel, and a healthy dose of random spew. (Everyone at 10NL has random spew, more than they perceive in themselves).

If I was Villain and I called, I'd smile that you had AKo in this spot. I'd smile cause I think you played PRE in such a way that you're going to end up misplaying the hand post almost every time.

Here, you represent strength, but you're holding the bottom of your range... weaker than you've represented... meaning you turned AKo into a bluff when you had decent showdown value.