Big All in from an opponent when I had K hit with AK.

There is no folding with TP/TK when the flop SPR is <2.

Vs someone who bluffs a lot, call, especially after you check the flop. He might have a set or KT, but he could have KQ, AT, QJ, or air.

What value hand would he take this line with?

Sets? 2 pair? This board is fairly dry (only one obvious draw) and not all that dynamic, so not much to "protect" from.

Also, I assume you checked flop to induce. Congrats! It worked! Now GII.

If I were to play this pot again, I would probably lead 4000 OTF. Generally, a board like this is going to check through, and you can't count on folks to put the money in for you.

What were his bet sizes when he bluffed before? Did he bet big when he bet with his value hands?

KK and 33 are unlikely. So is K3 or T3 although people do weird stuff sometimes.

TT is the only one that isn’t that unlikely, but does he shove the flop with TT? If you think the bet is big enough to look scary, wouldn’t you expect him to bet smaller or slowplay TT or two pair?

If it’s too big to bluff, isn’t it too big to value bet?

Easy call.

An easy question for me is what flop do you call with after 3 betting AK if not this one? Obviously it's not the absolute best flop for AK but it's pretty damn good. If he flopped better with a hand he shouldn't be in with or shoved middle or top set then good for him. He gets the money.

Thank you for your opinions. I called and then I lost. The opponent had K10s. I thought that he would be all in with KQ and KJ, and perhaps it might be air bluff.