So lets address all this stuff one little piece at a time.
Pre-flop: Everyone has folded to us and the SB, a "limping machine" (thought I am suspect of this since you already said you don't really know anything about him). So we are in position on the only other player in the pot. What we want to do is to get as much of his money as we can, with some secondary concerns that maybe we can address later.
If that is the case, then why did you bet pre-flop? If you want to say it was to bluff him, I guess thats okay - but you are in position and he isn't likely to fold. If you were trying to get him to put more money into the pot for value then you have a bad hand, its worse than the average hand. So you can't be doing this for value and you can't be doing it to bluff, because you know he is likely to call (limp machine is probably going to call a single bet).
What you have done is to create a pot that is bigger than the hand you are likely to get. This means that you are creating a bad situation for yourself later, your hand is going to be strong enough to really commit and if he applies pressure you will have a hard decision to make.
The best move, form a hand planning perspective, is to check and see the flop. You can try and take his money when you have more information and he acts before you. No problem. Once you have more information on this guy, then you can start to do clever stuff like betting with a J3. As it is you bet, so now we have to figure out how to manage that. for future reference don't do what you did here again.
What do we think the Villain has? It could be almost anything. like 60% of cards. It could be a pocket pair he is slow playing, it could be suited connectors, it could be a Q7 or a J8, who knows. Our play here has given us no information.
Flop: So now the flop has hit and you have two pair. Hey, this is THE BEST situation you can get for your hand. A flush is not really any better and a set is pretty good, but if they are betting into you then you may be second best. So with this hand you correctly bet, your bizarre gamble paid off. Once you bet he check raises. Now what is he doing this with? Well we don't know. Becuase we don't know anything about this player. It could be a bluff, it could be for value, but it doesn't make much sense. He has limp called/check raised this hand. Given that line I think he thinks he has a "good hand." I don't know what he thinks a good hand is. Is it AK, because this is a pretty thin board, is it QQ and he thinks he has us? Is it 7T and he is trying to "semi-bluff?" We don't know, because we have no useful information. So we have to play this game on level 1 of poker - what is my hand, how good is it relatively, and can it get much better? We have the 5th best hand at this point. And our hand is not likely to improve. There are few instances where something is beating us now and we will draw to improve. Given that is the case, we have to decide what to do.
1: Calling - calling is not a great choice, we don't get any new information and we set ourselves up for another tough choice on the turn. We are not pot committed and may be in a worse situation (rarely a better one) when the next card hits. I would never ever ever ever call here.
2: Folding - this has some merit. We don't really know what this guy is thinking and we have a middle strength hand that is not likely to improve and we don't have so much money in the pot now that we can't fold. You minimize your losses if you lose, but you are throwing away a hand that has value. It is a decent hand and given his range you are likely throwing away the best hand if you fold. I would likely not fold.
3- Raise - your hand is decent and not likely to get better, he may be willing to commit with a worse hand and that is good for us. It also sets us up for an easy decision on the turn. If we bet big and he calls we can pretty much keep going regardless. We make our job simpler by setting things up to make sense. I would make a fairly large sized raise here. Bump it to $12-$15. He may call, and we may lose, but we have a chance of gaining some value. He also may call with some strange draw or just a much worse hand, and then we got him to commit and basically donate us money. Raising I think is the best answer to this problem.
You are probably thinking to yourself, but I don't want to raise big here, this hand isn't that strong! You are kind of right, this hand isn't that strong. THAT is the reason we don't do those silly bets pre-flop, we put ourselves into situations where the only answers are crappy ones. Raising is the best answer in this situation.
The BEST BEST thing to do is not be in this situation. don't bet pre-flop when we have position and no information. Then, we can make more educated and better decisions on the flop.