This isn't a physics question, it's a geometry question.
The bike rides on air, and is supported by a force equal to the pressure x the area of the contact patch. Since the ground is flat, and the tire is donut shaped, the tire distorts until the contact patch is the right size for the rider's weight and tire pressure.
imagine cutting a slice out of the rim of a donut and looking at the area you've exposed. The larger the donut, the less in from the edge the cut has to be to expose the same area. Likewise the tire, fatter tires make a larger contact patch with less distortion, and so can run at lower pressures for the same load.
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Last edited by FBinNY; 07-22-14 at 04:40 PM.