[timprov]

I wouldn't want to be calling a raise on the end with jacks up all that often, and I'd almost never bet jacks up if I didn't know I could fold to a raise. If you feel the need to get to showdown against a tricky player, why not just call the 3-bet and check-call the end?

I think you're better off by check-calling anyway. The only spot betting is better is if he's drawing one with one pair or a bad two pair and will call you. Inducing a bluff seems like a better chance to get some value.

The problem is, you're both representing a good two pair or better. You need a parlay of both him to be lying and him thinking you're lying for your bet to have value.