Thanks for the in depth analysis of the hand. I agree with your thought process and I like the angle at which you are coming from, but I dont think I am missing too much value going with the smaller sizing if we want to give the villain some credit. Its hard to believe that I am floating his flop raise with air. Therefore if I bomb/bomb turn and river it would be obvious to any good player that I caught the jack (or the flush on a spade river). I think that a value bet sizing looks more desperate and bluffy. What do you think?

Agree about your perceived flop calling range not containing a lot of air.  By the river probably the worst hands in your range are 10x hands{ex. Q10, 109), maybe some 6x hands with a back door flush draw that bet/called the flop too.  His river call with his hand is very optimistic to say the least considering all the hands in your range that improved or have reasonable showdown value on the river. 

I think the turn is probably where we get most of our value against his bluff catchers.  Would you really be betting this turn with that sizing, ~40%, as a semi bluff/blocker/semi value with a lot of our medium strength hands, draws?  I think you would just be value cutting yourself alot of the time against him or just putting money in bad.  I think I have a wider check back range in this spot and prefer betting a smaller betting range.  Probably betting larger with some of my strongest Kx hands and Jx hands and balancing it out by bluffing with some of my weakest draws.  Checking back most of the other stuff in the middle.

I know I posted in my OP that we can bet big on the river as well but on this river thinking about it now there just isn't enough air in our range or weak hands we would want to turn into a bluff using this sizing.  Still don't hate it as people just love click the call button when the better bluffing cards for their opponent run off.

You pose a very interesting point. I think for the most part heads up play/bet sizings can differ greatly due to play style differences. I like what you said about my play style where I am very conservative with my continuation bets so when I do bet I should make them bigger. The obvious argument for betting small is so that future street bluffing will be cheaper. Playing deep in these heads ups added with my play style, I agree that I would have been playing more optimal with a bigger cbet sizing. Thanks for the observation!

1. Most of the time I do not base my decisions too much on timing tells as most players are multi tabling. At times in deep spots I will take it into account but it is very rare.

   1. I do float at times vs weaker players with very little equity (backdoor equity) at times if I peg them as the kind of players who 1cbet gives up.