Villain is pretty solid. Plays 21% of hands and has about 2 aggression.

I felt that if I bet out the flop and he raises me, I would know exactly where I stood. His turn check confused me and after the river, the only thing I really thought he had was a missed AK or AQ or actually JJ for quads. For some reason, I didn't think he have a different pair. Anyone not call the river?

Party Poker No-Limit Hold'em, $0.5 BB (9 handed)

Button ($42.03)
Hero ($50.1)
BB ($19.9)
UTG ($35.25)
UTG+1 ($60)
MP1 ($35.2)
MP2 ($51.4)
MP3 ($36.85)
CO ($12.75)

Preflop: Hero is SB with , .
UTG raises to $2, 6 folds, Hero calls $1.75, 1 fold.

Flop: ($4.50) , , (2 players)
Hero bets $3, UTG calls $3.

Turn: ($10.50) (2 players)
Hero checks, UTG checks.

River: ($10.50) (2 players)
Hero checks, UTG bets $4, Hero calls $4.

Final Pot: $18.50

Results in white below:
Hero has 3c 3s (two pair, jacks and threes).
UTG has Jc Js (four of a kind, jacks).
Outcome: UTG wins $18.50.

turns out, i'm glad I checked because he gave me a free card to hit my outs and I only had to call a small bet on the river.

Hmmmm... This one is a little tricky, although I don't like your opponent's play at all. Here are my thoughts:

Ok, that flop is dangerous in principle, but not against a raiser with big cards of some sort. I still think you bet it out too passively. If anything, I'd overbet the pot just a hair, but certainly full pot. On a semi-bluff, you need some fold equity imo.

I don't like his flop play either. I think he needs to raise here. You can actually have a very wide variety of hands (overpair, set, straight draw, made straight, two pair), and he needs to find out which one it is. In any case, I think the flat call makes AK/AQ less likely--not to say non-existent at all, but it's a horrible play of either of those hands. It's just that your weak flop bet doesn't fully put those hands to the test either imo. Anyhow, I think with only one card to the straight, you're going to have trouble getting paid much on the straight, so you want to take it down right here if possible. This actually isn't the greatest semi-bluffing opportunity for the same reason, but I don't mind trying it.

In any case, after the call, I'd probably be putting him most likely on 99-QQ. While it really doesn't matter much which one it is on that flop, people are much more inclined to raise AA/KK there. You could also have been flat calling with QQ, so I guess there is some rationale behind it

I'm sure that some will disagree with me here, but I actually do like your turn check. True, you can represent a set or the made straight, but you've already made your semi-bluff, and, without improvement, I just don't like to get in any deeper. Quite aside from his making the set, is QQ (or even 99 or TT) on the same board seriously going to lay down at this point? Even if this player hadn't improved, I think he was planning on just passively calling you down with his overpair. In any case, a check on the turn allows a second mistake on the part of your opponent: Giving you odds to draw. Had he bet very much, I think you'd have to fold, however, since with only one card to the straight here, I don't think you'll have very good implied odds (the deuce will actually help you more than the 7 imo).

His turn play is absolutely horrible, I think--typical slowplayer. Maybe he's still scared of a straight, maybe he think he has you oversetted and is confused that you didn't bet into him on the turn. But it amazes me that he doesn't bet here. On the basis of this hand as well as your comments, I'd classify this player as tight-passive.

I also think I would fold the river after all that. The bet doesn't seem like much, but I think the chances of his having some kind of big pair (maybe 99/TT, maybe QQ) are pretty fair. JJ is also possible but less likely, but 99 already beats you. Moreover, this is a bet that wants a call, and, having missed your draw, I don't think you have enough hand for a crying call here.

The AK/AQ theory is also possible, but I don't really have a problem in laying down the best hand in that situation either. You made a weak semi-bluff, he called and allowed you to draw. You missed on both turn and river. So, I think you're simply done with it. You're really not "proving" anything by making the call, even if you do have the best hand, and I doubt that you do most of the time. The whole betting sequence, as well as the unusual flop situation, I think tend to lead away from the old "set it or forget it" idea, which is in principle sound--even if they're playing an unimproved AK aggressively.

I guess to summarize my opinion: If you're going to semi-bluff, you need to bet aggressively, then you go completely into the defensive unless you make your hand. It's actually tricky to do out of position, but he misplayed the flop and turn imo, allowing you to draw. But that's no reason to pay him off on the river.