From Sheldon Brown:
All About Bicycle Tires and Tubes
Width and Pressure
Tire width and pressure are inextricably linked. It is a serious mistake to consider one independently of the other. Generally, wider tires call for lower pressures, narrower tires call for higher pressures.
Consider, for example, a tire one inch across, at a pressure of 100 PSI (pounds per square inch). Air is pushing down against the bottom half of the tire cross-section with a force of 100 pounds per inch of length. Each sidewall of the tire bears half that load, and so inch of length of tire sidewall will be under a tension of 50 pounds. Now let's consider a tire twice as wide, two inches across, at the same 100 PSI. Each inch of sidewall will be under a tension of 100 pounds. So, a wider a tire would ride harder, and need stronger fabric, if inflated to the same pressure,
The part of the tire that is actually touching the ground at any moment is called the "contact patch." Generally, the area of the contact patch will be directly proportional to the weight load on the tire, and inversely proportional to the inflation pressure. For instance, if the rear tire of a bike is supporting a load of 100 lbs, and the tire is inflated to 100 PSI (pounds per square inch) the contact area of the tire will be roughly one square inch. If the pressure is reduced to 50 PSI, the tire will squish out until the contact patch has become 2 square inches (or until the rim bottoms out against the tire.)
A common debate among cyclists centers on the issue of whether a wider tire has more or less rolling resistance at the same pressure. The constant pressure is proposed because it appears more scientific to eliminate this as a variable, but this is not realistic in practice. The short answer to this question is that, yes, a wider tire of similar construction will have lower rolling resistance than a narrower one at the same pressure. This fact is, however, of no practical value. If you are comparing two tires of similar construction, with the same load, and the same pressure, either the wider tire is overinflated, or the narrower tire is underinflated!
A tire is supposed to deflect a bit under load. This deflection the whole purpose of pneumatic tires. When you sit on your bike, your tires should visibly bulge out at least a bit under your weight. If they don't, they're overinflated.