You're pretty close... I'd opened my 3-bet shoving range against your raises a lot. Mainly because I didn't expect you to be able to call with a lot of your holdings so I expected my fold equity was higher than usual.
The range I was shoving there was: 55+,A5s+,K6s+,A9o+,KTo+ which you have 43% equity against.
K6s is the bottom end of that but I'd already decided I was going with any suited K-nonwheel.
lol, I bet you thought I was going to make up a range that would have your play be bad. I don't think it was. I just wanted to see if you knew it was a decent play or not. I was shoving medium pairs, strong offsuit Aces and Kings, and marginal suited Aces and Kings. No Queens because I expected I might need the power of a high-card in show-down if called.
Against my normal range with those stacks and blinds, A9o would be a 34% equity hand in that spot. But with the amount of chips you were committing (which made a resteal tempting) and the frequency you were doing it, I had widened my range to a point where I thought it would be profitable -- when fold equity was computed into it.
Against a small raise, if it's sure to be heads up, I might call with AA or KK... and hope to extract some value by playing a small to medium sized pot on the flop. But against a big raise (10% of the effective stacks or more), I'm almost always shoving pre-flop here. If you go along for the ride, I'm happy. If not, the pot it large enough to make me feel like I got some value from the big pair... and without risking a bad beat. I'm not saying I never call in that spot but I'm much more likely to just put the chips in pre-flop while I'm certain the hand is good.
That said, I don't think you played poorly. I was just shocked you called that much of your stack in that spot. And then flopping good... and losing anyway... that sucked. But that's poker.
