Parents who seem overprotective are often like that because they know what young people can get up to. Parents were once young themselves, and they very likely remember what it was like to sneak around behind their parents’ backs. (For some of them, this might be about the time they first became parents-to-be.)
On one hand, they’re just trying to protect you from what they know can and will probably happen. They want the best for her (and you-as-a-couple) and that might include making sure you don’t mess around too early. This is not weird,it’s just what responsible parents do.
On the other hand, of course you’re going to want to test the boundaries and push the envelope a bit. That’s what being young is all about, too. If you don’t screw up in life a little bit, you won’t have as many experiences to (1) learn from, and (2) look back on fondly when you’re old and nerdy, possibly guarding the virtue of kids of your own.
I think the key here is, just be respectful of them and understand that they know what you’re up to, and have a little fun anyway. :) (By fun, I don’t mean anything that can get you into trouble. Think about it.) If you/she are under a certain age, remember that they are responsible for what you do, too, both legally and ethically. If you both prove that you are responsible, respectful, and can be trusted, you’re likely to be trusted more as time passes.