Well, the idea is nice, but, as others have said, we need to account for sidewall stiffness. But we can do better with law of large numbers and employing metering tape to measure difference in car height with different pressure in tires. First we need to collect baseline data - tire brand, model and size, tire pressure, and car height difference , for known car weights, for two different pressures (say, 20 and 35 psi), this way we could deduce tire sidewall stiffness for given make/model/size of the tire. After that we can do the same for all cars with same tires, by measuring car height difference between two pressure points. Measuring height changes on both axles (wheel center to lowest point of the wheel arch) will get us weight distribution ; but we'll need to account for staggered tire setup .
