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Maybe you could use sandpaper to make a small flat spot on the tires where they contact the "ground" to give an impression of weight?
Look at a real truck or car, even if the tire doesn't bulge sideways there is still a small flat area where it rests on the ground. On a normal car with normal load and tire pressure the flat spot has the size of a palm or maybe a little more (depends on the size of your hands
On a truck it will be larger, maybe two hands, palms + fingers.