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I'd bet and fold to a raise if I didn't improve.



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Nah, assuming the river card isn't an overcard to your jacks, you need to adopt a plan that assures a showdown. Top pair top kicker has too many ways to win to fold on the river in this situation. Maybe you check call, or make a crying call of the raise. Either one is a better plan than bet/fold in my opinion.

In your original post you said you're trying to learn to become more aggressive, and your turn play is a fine example of your efforts to improve. I think you may have a river leak, however. As you become more aggressive, people will believe you less. The result is that, ironically, you must become a bit more loose and passive on the river in certain situations. Don't become weak at the same time you become more aggressive.

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I had position on my opponent in this hand. I would be VERY surprised if he would check-raise me twice in a row after I 3-bet the turn with a hand worse than AJ.

edit: however I do agree that I need a plan to see a showdown no matter what. I think in the heat of the moment I probably would have bet/called a checkraise, not that that is correct.