Bathroom scales ftw!
Here's a stab at it, although I think your best bet is to have it done professionally:
Fabricate four big, sturdy wooden boxes. Maybe about 6 inches tall, 12 wide, 24 long. Find a very very dense clay. I don't know if play-dough would work. I think it's compressibility forgiving. The reason I like play-dough is that you need soemthing that will not dry out in a matter of a few days. Top out your wooden boxes with this low-elasticity agent. Cover the top with some sort of sheet of rubbery-plastic material. This is mainly to reduce how much air makes it to this mystery dough, thus avoiding premature drying.
Jack up the car. Place one of the four wooden boxes under each wheel. Lower the car unto the boxes. It would be best if all four corners are lowered at the same time/same rate. However, this is not critical. Label the boxes according to what wheel they are holding.
Let the car sit on the boxes for a few days. This will reduce the impact of any error introduced when the car was lowered, since all wheels will most likely not be lowered at exactly the same time.
Jack the car up. Remove the measuring instruments (what I have been calling boxes so far).
Find an accurate (very accurate) method to determine how deep the impression left on each box was.
Post those figures. Using physics of moments, we can determine which axle had more weight on it, and to what proportion. In fact, if we know the compressibility figures on the special mystery putty, wwe could even determine the weight in lbs.
This should work in theory. It seems to me like a lot of work, especially because I have mentioned a couple of unspecified materials and one mystery measuring instrument. Furthermore, the wooden boxes should have to be really really sturdy. Otherwise, the load on each wheel could push out the mystery putty to the sides, and completely break whatever box you buil, unless it has a lot of nails. Thick metal would be better, but I doubt you have something like that in your garage.
hint: I believe you can determine the specific psi rating for the mystery putty by determining the area of your tires' footprint in square inches, then estimating about 800 lbs/wheel. Whatever number you get from dividing 800/(footprint square inches), find a material with about 75-85% that psi rating (to allow for the car to sink in).
If this works. Then let me know. We can publish a white paper or something.
With all that said, just give it up buddy