There is an engineering explanation to what you are describing. With air-filled tires, the inflation pressure equals the average pressure exerted on the soil regardless of how much weight the tire is carrying. Adding more weight without increasing tire pressure means the tire has to bulge out to have more surface in contact with the ground. In other words, the contact area increases but even though the pressure stays the same you can carry more weight. (With really stiff-walled bias ply tires at low inflation pressures this rule breaks down but within reason it is accurate. The rule assumes the air, not the tire carcass, is carrying the weight.) However, with fluid in the tires, you gain the weight of the fluid which exerts around 1/2 psi with every foot of depth. So, if your tires are inflated to a level 4 feet above the ground, you gain 2 psi of soil contact pressure for the same inflation pressure and the same amount of tire bulge.
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