If river is the 2c, I value bet this all day. Def a check when J hits though, really tough for villain to have a calling range otr that you're making money against.

You should have the best hand almost every time, but vbetting is very thin and depends heavily on your history and esp this particular's session dynamics. You said you have battled a bit, well how did those battled end should determine your play on the riv. You have to ask yourself how often did you get to showdown with him, what hands did he saw you show down, how likely are you to bluff that riv and what's your perceived range here.

But first of all what kind of 3bet size is that? Is this his regular sizing? 

Agree with the above...this looks like a very clear check without more specific context/history. I can think of very few worse hands that will call and very few better hands that will fold if we bet. I'd imagine most of his jacks-up will have a blocker or two to the straight and very inclined to snap you off when both FDs miss.