Do you have a tire gauge? Have you had pinch flats when you've hit bumps?

What kind of tires do you have? What surfaces are you riding on, and how hard are you cornering? Knobby tires can feel very unsteady on pavement when you're turning with an extreme lean angle, so that you're beyond the tread on the sides of the tire.

Tires are part of the suspension system on any vehicle (the only suspension, on a road bike or hardtail, other than your own body), so they will compress somewhat under your weight. But they shouldn't seem flat. How does the tread wear look?