Check the pressure, don't guess. Check the pressure regularly...every time you ride, at least to start with, until you get a feel for how quickly the pressure drops. Bike tires lose pressure rather quickly, enormously faster than car tires.
Consider an idealized case, with some rather crude approximations: Take a tire inflated to 100psi, and touch it to the ground with absolutely no weight on it, not even its own. It'll touch the ground at a single point, with no flattening at all. Now, apply some force...say, 100 lbs. The tire will flatten somewhat to support that force. How much? Well, neglecting most of the real world, it'll flatten to the point where the contact patch touching the ground is about 1 square inch (it's mainly the air pressure that's supporting things). Now increase the force to 200 lbs, and the tire will flatten more, until the contact patch is 2 square inches. The tire has to flatten in order to support any weight.