[Leo M]

Eventually you get the equations:

Fa = W/(1 + Ra/Rb)

and

Fb = W/(1 + Rb/Ra)

and it is unnecessary to make any assumptions about the location of the CG, other than that it lies between the wheels.

Substitute the distances Ra and Rb into the above equations, and out pops the force distribution on the wheels.

If we further assume that the wheels are a distance "L" apart,
and the CG is a distance "H" above the line of the axles and centered between them (with the body horizontal), and the body makes an angle A with horizontal, then we have for Ra and Rb :

Ra = ((L/2) - H tanA) cosA, and
Rb = ((L/2) + H tanA) cosA.

(Check behind me - I did this quickly on scrap paper.)

Now you only need to know how wide the robot is, how high above the axles the CG is (good luck, but try to estimate), and what angle the body makes with the floor, and you can calculate the weight distribution. If the CG is not centered, the geometry is a little more complicated, but not that bad.