at what point can I fold in this hand? or should I be? I was going to fold the river because I would just assume that most bluffs would give up then, but then he's like lol-halfpot and I suckered myself into calling.

villain is acting a bit weird playing 71/38 over 21 hands
somehow he has otherwise escaped my keen observance

fold turn?

villain dependant. against some players i fold flop, against others turn.

either flop or turn

fold flop, there are 0 draws, and higher Ax very rarely raise the flop for value

also therefore this is a decent bored to check behind (like 1/10 times?)
or against retarded regs who always barrel when checked too

Obv villain dependent, but Id almost always fold turn. Against some Id call flop because they would shut down on turn with bluffs (and they actually have bluffs on that board).
The problem here is that the board is so dry that if they get called with a bluff they are rarely going to go through with the bluff on the turn. Just look at it from his perspective, you cb/called on a Axx board. Does it look like you're going anywhere? Do people like folding AQ/AK type hands? Nope.

On the other hand, he IS a 71/38 albeit over few hands. Id still fold turn though.

You beat A7 and 45. Formulate hands you can beat and what hands villain would raise then make your decision accordingly. This just seemed like "Well, I have AJ on a dry board and my Jack is a decent kicker so I think I'm good here."

umm why would you call river as played
turn is a fold