if we check back the turn we check back the river unless we hit one of our outs
if a J or A hits and we get checked to we shove

and to be clear i think the only reason we'd ever check back the turn is the board pairing like it did, if it bricked (or the top card paired) I at the very least would be barreling

This is very true.

If a jack comes on the river there is no way I am shoving once it is checked back on the turn. His calling range will have me crushed here and my hand won't play well enough against his range imo. The only thing that villain will call me with that I may beat is 99 or KT,QT maybe. Most of his range has me beat. I think I would play for showdown value. If an Ace hits the river than I definitely shove.

The only thing I can do to barrel the turn is bet more on the flop (60ish) and then shove the turn which is a better line than what I took. My stack was too small for my bet sizing as played. But I am not crazy about barelling all-in the turn with 12 outs and one pull of the deck. To me my bet would still look like it was FOS because it would not appear as though I was attempting to get any value out of my hand. I think a turn shove can look bluffy here. Would I fold out my opponents overpair enough to make this play profitable? Now if I was holding AK I may feel differently about this.

Not knowing anything about villain its really hard to say.

If i landed in that game cold, then i would most likely raise flop to only $35 or so. Villains cbet was small and all we get him off is air with a raise anyhow. Its possible villain would call this raise with AK and fold to a turn bet of say $40 too which would be awesome. then check river if called.

yea no one is folding that turn card after calling your flop raise, unless you have a read that villain is super nitty. Take the free card on the turn, difficult to say if villain is c/c with worse if river is a A or J? dunno prob value bet small ish try to get calls from small over pairs.