I think you need to be re raising pre flop with AK, especially when OOP. You guys are playing deep this means that position becomes more important and your post flop decisions which are harder for you - due to you being OOP - are more important.
You can profitably get in AK preflop for 100 bb against random 2nl players. I'm not too sure about much deeper but it is still probably ok to get stacks in here.
I think this board is wet enough for us to donk with TPTK, villain will probably call us with all flush draws, all straight draws and all pairs. Checking here is dangerous as there are a bunch of turn cards that will either make your opponent a better hand or scare away your action. The only time we can consider checking is if villain is loose aggressive and we plan to check-raise them, so I believe we must raise villains C-bet.
As played I think we need to donk the turn as well, as I said before there are a bunch of worse hands that will continue. And a bunch of draws that will take a free card if we check. I think it is unlikely that villain is betting a draw very often again here. I believe that they are betting for value, but given this there aren't many value hands in villains range that you don't beat that are 3-betting preflop, my suspicion here is that villain might be value betting a hand like KQ or QQ. Their range does include all the premiums but I think that their value betting range includes enough second best hands for us to call. Especially given how under-repped our AK is.
River is an easy call, you now beat so much of Villains value range that would be shoving here that we fist pump call. There are also a few missed flush draw bluffs that villain decided to barrel.