A hand problem

Here is a hand I played yesterday and when I looked back on it, I didn't really I played it well or not:

Villain raises to 10 BB ($0.20) in MP and it gets folded to me.
I'm on the cutoff with pocket queens and I decide to reraise to 25 BB.
I had two reasons: the intial raise was pretty big and I wanted to know if I was up against Aces or Kings, and I didn't want anyone behind me to enter the pot.

Villain just calls the reraise. I really think he would have reraised me if he had Aces or Kings because he was out of position. Since, I don't think he would have raised with small pocket pairs or called with hands like AQ, AJ, I put him on QQ, JJ, TT maybe AK or a smaller pocket pair.

The flop comes 10, 7, 2 rainbow and he checks it to me.
At this point I have about 120 BB left (villain has me covered) and the pot is 100 BB and I shove it. At the time I thought I was very likely to be ahead (unless he did have Aces or Kings or made a set with 10's). He called and showed a pair of Jacks and I took the pot.

So even though I won the hand, I'm not too sure I should have shoved there. I would not have called the push with Jacks so against a better player it might have been better to bet less to induce a call?

What would have been the right play if I had had 200 BB or more behind?

Feel free to comment...