Quote Originally Posted by Massimo
The thing is that poker is really simple and the solution isn't complicated if you look at this in a different way.

I think what makes you stuck here is you're looking at an individual hand. Ok, against a solid player like JEM it's unclear whether you should bet or check. But, in poker, you just need to look at ranges and adjust them If he's folding too much, like you think, you should be bluffing this spot more. This is the solution.

Given the neutrality of AK here with your reads, you're basically free to do whatever you want as long you doing that action doesn't encourage him to adjust his ranges in a way that isn't beneficial to you (aka has bad metagame).
This is essentially what I was getting at. I don't think he's folding "too much" on the turn. I think that because of the very high % chance that he calls all his nut hands on the flop that this is not a great board to double barrel bluff. It is obvious that he will adjust his ranges versus a turn check in a way that will be very beneficial to me (a. He will check behind a medium to weak range, b. he will bet his strong hands and bluffs.). On the other hand, his range is still so wide on the turn that betting the turn and possibly river seems like suicide.