Everyone else has addressed the preflop (which is a leak of mine - just had some flaws in my 3bet thinking pointed out by spenda and BJaust this morning). I'm curious why you bet the turn? After 3betting and get called on the flop, what hands could he have that you beat?

This is an interesting spot for me because we would get MORE information from NOT betting here. (I detest "bets for information" but that's a whole other post.) The pot is about $3.70 on the turn. He has $5.80 left. When you bet $2 and he calls, it sets up a half-pot river bet that tells you nothing other than you're beat. But he's read you for some strength and a willingness to get it all-in, so his bet is automatic, and perfectly sized because YOU manipulated the pot for him.

If you check behind, he's got an interesting decision. Now, the pot is $3.70, and he can't get all his chips in without overbetting the pot about 1.5x. Also, with a check behind on the turn, you've shown some weakness, so he's not really sure if you'll call an all-in bet.

He's got 3 options basically:
1. Half/two-thirds value bet around $2
2. Pot-sized bet around $3.50
3. All-in shove

Each of the three reps a bit of a different range. I think the key thing to notice is that the overshove (#3) is incredibly easy to get away from, so it's unlikely that he'll try it. He'll probably try #1 trying to get more value from his hand, and you risk less overall.

I know that we don't wanna call the river here, regardless of additional information (since we know we're pretty well beat before the river), but the point I am making is that you destroyed any chance you had of learning more about his hand with your turn bet, and you made it easy for him to play his entire range correctly against your range. When you do have equity in a hand like this but are uncertain where you're at, planning ahead can get you the extra information you need to play the river correctly.

Quick overview of your game: you're making a mistake I used to make all the time, playing each "street," not planning out the hand. I used to think in terms of "I'm probably behind, but a bet here could (might) take it down." Now, I try to think what will happen on the next couple of streets if I bet and get called, or what I'll do if I get min-raised, or shoved on, or donked into, or whatever. Of course, that means I think of what villain's range is and decide how he might play each part of it, and the "range range range" mantra has already been pounded.

I think you need to consider ranges AND plan your hand based on those ranges. Try to think one whole street ahead, and try for more streets as you get more practice. It would have saved half a stack in this hand had you considered the river while thinking what to do on the turn.