Yes, all of your bets here were weak. That's the entire reason he pushed against you, however...so this same style could almost be employed intentionally. A better line would be to make it 1,75 preflop, then bet 2/3 pot on the flop. If he calls, you can probably push the turn given your small stack.

For the first time ever, I'm going to say that yes, you did have too short a stack. The reason, however, isn't because of how much your stack was. It's because you asked. To play standard NL poker, you want to have a max buy-in. If you're playing short stack (which can be fine; can even be very profitable), you want to know your reason for doing so. Kinda like how you played this hand was a mistake, but more because you didn't know why it was a mistake than because of the play itself.