You have to know where the center of gravity is. If $a$ is the % distance along the wheelbase for the center of gravity (50% = center, 0% = front, 100%=back), and $b$ the % distance along the track for the center of gravity (50% = center, 0% = left, 100% right) then the weight fractions for each wheel are:
$$ (\mbox{front-left}) = (\mbox{Weight}) \frac{3-2a-2b}{4} $$ $$ (\mbox{front-right}) = (\mbox{Weight}) \frac{1-2a+2b}{4} $$ $$ (\mbox{rear-left}) = (\mbox{Weight}) \frac{1+2a-2b}{4} $$ $$ (\mbox{rear-right}) = (\mbox{Weight}) \frac{2a+2b-1}{4} $$
There equations come from the balance of moments in two planes. Here is a top view of the balance.
Example:
I the front back-balance is $a=0.4$ and the left-right balance is $b=0.55$, with a chassis weight of $0.5\,{\rm kg}$ then the corner weights are:
$$ (\mbox{front-left}) = (0.5) \frac{3-2*0.4-2*0.55}{4} = 0.1365 {\rm kg}$$ $$ (\mbox{front-right}) = (0.5) \frac{1-2*0.4+2*0.55}{4} = 0.1625 {\rm kg}$$ $$ (\mbox{rear-left}) = (0.5) \frac{1+2*0.4-2*0.55}{4} =0.0865 {\rm kg}$$ $$ (\mbox{rear-right}) = (0.5) \frac{2*0.4+2*0.55-1}{4} =0.1125 {\rm kg}$$
Results Check
- Total weight on left wheels = $0.225 {\rm kg}$
- Total weight on right wheels = $0.275 {\rm kg}$
- Left-right balance = $b=0.275/0.5 = 0.55$
- Total weight on front wheels = $0.300 {\rm kg}$
- Total weight on rear wheels = $0.200 {\rm kg}$
- Front-back balance = $a=0.200/0.5 = 0.4$
- Total weight = $0.500 {\rm kg}$