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I would have check/raised the flop, I'm somewhat surprised by everyone bet/3betting

IMO when you lead a lot of players are smooth calling with AK here

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Ditto. That combined with his low PFR made me think a 3-bet would be very -EV. Would be a bit different if we were holding QQ+, but when we only beat 99 or overs, I think a check-raise is the way to go.

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You think that people will smooth-call with overs, yet fold to a c/r on the flop? The fact is that someone with AK is very likely seeing the turn either way.

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No, I don't think he'll fold to the check-raise. But I think that a) he'll bet his overs on the flop if we check to him, and b) he'll hardly ever 3-bet our check-raise with a worse hand, which means we can check-fold the turn those times he do 3-bet. It would be different if we had QQ or better imo.

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We are lead betting because there is a decent chance we are ahead and, if given the opportunity to 3-bet, we want to take it. After 3-betting, a lead turn bet might finally make the overs fold (not to mention get a bigger pot for us).

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Although he sometimes will raise overs on the flop, he will not always do that, meaning that when we bet and he raises we're not 100 % sure where we're at. At the same time I don't think we're ahead often enough to 3-bet.

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And perhaps most important, if we 3-bet and lead the turn, it is much easier to assess the strength of our hand thereafter. If you check/call the turn, how will you have any idea whether you are ahead or not?

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Who said anything about check-calling the turn? I was advocating a check-raise and lead on the turn if our check-raise is called, which it will be. If we're 3-bet on the flop I was suggesting that we check-fold the turn. The information you get by bet/3-betting should be the same kind of information as you get by a check-raise against a player with this stats.