It's important to know when it's appropriate to start shooting second and third barrels. You clearly misjudged the situation and misplayed the hand this time.

If you continue and get a call, then you need to assess WHY your opponent called. Ideally, you hope your opponent is overpaying for a draw that will miss, or calling with second or third pair. Is your opponent capable of calling with second or third pair? Have they done it before? If they have then it begins to justify a second barrell.

Since you had two jacks, the straight is not likely. You disregard it. That leaves a flush draw. It's good to know how aggressive/loose a certain player is. If you had seen him min bet or semi bluff the flush draw before (as a lot of players do), then you might read him as NOT drawing to a flush since he just check/called. That leaves a hand that beats you. There's your read in some cases.

It's not always correct to bully someone off when the board beats you. Just keep charging them for cards if you think you're ahead and take your 60-65% favorite to the river and go from there. I don't worry about pricing them out if there's a fair chance I'm behind. Sometimes I convince myself I have no right to price them out with such a slim vulnerable holding.

Often I will recognize there's a good chance I'm behind and duck away. Maybe that was the best option from the flop forward here for you. I don't blame you for putting him on a flush draw if that's what you decided, but I would blame you if this method was born of blind disgust over a simply beaten JJ.