It's a great board for him to bet at on all streets. Neither you or the later streets have given him a reason to slow down, with just a call pre flop he can narrow you down and eliminate ak from your range from the equation, after that i think its a question of low pairs.
Since you didn't raise the turn which is when you would probably be raising 22. He can then narrow your hands after the call on the flop to 33,44,55,66,77,kq (not sure on your stats so unsure how accurate this calling range pre is for hero). A lot of the hands mentioned you would probably represent on a king high board with a float or a raise but on the turn your hand becomes very transparent and the range becomes very definitive with the second call.
After that it's just a case of leaning on you on the river whether he has the goods or not. I think you 1 of 3 different lines here.
1. raise/fold the flop
2. float flop - fold turn
3. float flop - raise/fold turn
I really believe call/call/call is way to passive, and a raise on either the flop or the turn is way to play and you can then fold safe in the mind you were second best. I think you get yourself in this position by cold calling pre-flop, 3bet/folding is the usual line i would take. Villians stats are very very similar to mine so i'm trying to look it from my perspective, the board is perfect for a triple barrel, but i'd need to see your stats for a definitive line.
Interestingly i was discussing KQos with another grinder and he believes calling in position is the right play as 3betting forces the villain to fold a lot of weaker kings and queens. I personally find that the hand just gets you into too many tough spots you didn't need to be in in the first place but I'd be really interested to see what the hand evaluator says about this.
Apologises, i've never evaluated a hand on the forums before, hope i went about it in the right way. cheers