[Malachii]

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the 3bet cost me a total of $8 more than my inital bet. I immediately find out if he has a hand or not

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No, you don't. If he calls, he could be calling with an OESD, a set, or better/weaker queen.
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- If I call and then bet, it's $2 to call, and then the pot at the turn is $10. I can bet about $6-8 here, but it's the same price as the 3bet really.

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Yes, but if he calls then all you have to worry about is the river, and if he raises you you're done with the hand. If you 3 bet you have to worry about 2 streets.

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The basic question is then... how is seeing the turn going to help me?

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Because you want a cheap showdown, which involes playing the turn and river for as little as money as possible but without giving a free card to a straight draw.
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Could you elaborate more on why the call/ bet turn
is better?

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It's called a stop and go and it should be one of the tools you use if your flop bet gets raised and you have an overpair or TP/TK. Basically, lots of people will raise top pair, sets, or draws on the flop. Very few people will raise draws or top pair on the turn, so it keeps the pot small on the flop, helps you see a cheaper showdown, and gives you more information as to where you are in the hand.

Hope this helps.