Really interesting hand!
Trivial fold imo.

I'm going to write a few of my level 1 thoughts, please feel free to flame me if you feel my thought process is retarded.
Ok. To me turn bet wreaks of one of two things, extreme strength, or, well, come to think of it, nothing else really, just an attempt at looking weak. If you were weak you'd think you'd just check behind here. I know you say you'll balance it out with air, but it's almost ALWAYS this way round, ie you don't bluff first.
I'm guessing you guys are friends so he knows your never value betting 1/4pot nor betting this amount as a semibluff. Also by just calling otf your repping a made hand as you'd probably raise the flop with a strong draw. (although this snippet obv has less merit to previously stated dynamics.)
Just to go off on a slight tangent a second, but value betting 1/4pot to set up subsequent 1/4pot bluffs to pick up folds is, to my level 1 thinking, a pretty laughable theory. Unless of course you have massive history, and expect to play huge volume vs this villain? It could work against regs in mtt when you have relatively shallow stacks I guess, but not at deep cash games. What's the point in putting effort into getting the least amount of value from the nuts, to then bloat the pot with air as your giving your villain great odds to float/call with a marginal hand?
Anyway, back to the hand. I honestly think Mitch 'I always get there' Johnson has 9x here.
As its highly improbable for you to also have 9x, he has to have you on 56/TJ or a fh from reasons stated in regard to your turn bet. He's not raising you here as he knows he's pretty confident that he's behind, but will certainly call hoping to pair up as you've given him the odds to do so.
Once the river hits he checks knowing that you have to value bet 56/TJ/88/77, then gives you the right odds to be able to call his raise even on such a scary board. Also gives you enough room to spazz all-in.
As played this is way to scary a board to value bet imo, so I check behind with showdown value. Unlucky on how the board ran out.
My level 1 thoughts anyway! Ta