Why 3bet?

[Joost1982]

Situation:
25NL 6max, 6 players, all 100BB stack. Everyone folds to the button (with TAG stats, preflop raise 12%) who openraises for 4BB. You are in the SB with AJo. Now what?

Some people say you should fold here because AJo isn't that good of a hand, especially versus a TAG and in this position. However, it is an open button raise, which can mean that villain's range is much wider. So maybe you CAN play the hand. What is better then; call or 3bet?

A few months ago I always called, but lost a lot of money, because I had to fold the hand most of the times. The last few weeks I'm experimenting with 3betting and this makes my plays so much easier. A cbet on almost any flop gives me the pot.

But: what is the correct reasoning behind 3betting?

(1) you gain momentum? With a cbet you get the pot.
(2) you can find out if villain has AA/KK? (he 4bets).
(3) ...?

If villain has a good hand like AQ+ and you hit your ace what is less costly; a preflop call or a 3bet?

If villain has a better hand like TT-AA, what is now more EV, a preflop call or a 3bet?

A lot of questions, but they all relate to the same thing: why 3bet? (here)