The stiffer the suspension, the less the weight transfer. If you look at very stiff cars with one wheel in the air, there is no weight transfer to that wheel!
D. Clay is right, weight transfer is determined by 2 things and 2 things alone, track width and center of gravity height. For the engineers out there, this creates a moment arm between the force at the center of gravity and the contact patch. The weight transfer can be broken into 2 component, elastic and geometric. The amount of each is determine via suspension geometry and whats known as the roll center, or roll axis when dealling with the complete car. Geometric weight transfer basically corresponds to the forces that get put through you suspension members due to weight transfer, whilst elastic get applied through your spring; as such can be much more controlled. You will always have some geometric weight transfer, this can create whats known as jacking, which will lift the chassis of the car. But this depends on the roll center position being above ground.
The only way other then varying your track and center of gravity to change the weight transfer is by changing your roll stiffnes distribution. This will not change the total amount of weight transfer from one side of the car to the other, just which wheel it gets applied heavier to(Front or rear outer). That total amount of weight will get taken off the inside wheels(again changes with roll stiffness distribution).
This is bascially why adjustable anti-roll bars can be so useful. By varying the roll stuffnes distribution front to rear the over steer understeer characteristics of the car can be varied.
Anyway ill leave it there or ill waffle on for ages about it. There are dozens of more parameters that can vary what is happening.
Also lifting of a wheel can happen if a car rolls to far and the inner wheels hits its droop limit, while the car physically rolls more. Such a case creates a different behaviour in weight transfer of the car. Which would seem that increasing stiffnes decreases weight transfer. Instead increasing stiffness is changing the behaviour of the car to limit roll, to hopefully have the wheel not hit its droop limiter and hopefully not lift that corner. Once this is achieved increase stiffness will not change the amount of weight transfer. Many open wheel race cars run droop limiters not giving the car the ability for the wheels to drop very far. This doesnt mean they they are trying to lift the inner wheel though. It is actually a more complex behaviour all together.
