Raising in limit Holdem

If I re-raise the pot after the flop with a flush draw, what are the benefits of doing this?

If you have position, more than likely they will check to you on the turn. You can then check behind if you don't make your flush on the turn and get to see the river for free.

Look at it like this. if you play 3/6 limit, and 3 people call pre flop. You flop a flush draw. 1st guy checks, 2nd guy bets and you raise, guy 1 calls, guy 2 calls. (you have now put in 9$ in the pot) turn everyone checks to you and you missed your draw. River comes and you hit it. Guy 1 checks, guy 2 bets, you raise again. guy 1 folds, guy 2 calls.

Now take the same situation but this time you just call the bet on the flop,
3$ pre flop 3$ on the flop + 6$ on the turn (you have spent 12$ now to see a river vs 9$ with a raise on the flop)

It allows you to save half a bet to see a river.