Updated: May 14, 2021
Weight transfer and body roll are not directly linked, but where there is a lateral acceleration (i.e. cornering), you can be sure to experience both!
With the outside tyre presenting much more area to the track surface, the influence of body roll on tyre contact patch size can be seen clearly from the skid marks left by the LMP car in this beautifully shot photo. Perhaps more important though is the influence of lateral weight transfer on the coefficient of friction (CoF) between the tyres and the road surface.
The graph below shows the relationship between CoF and increasing vertical load.
Chart 1: Clearly, it's a non linear relationship between the CoF and reaction force; one unit increase in reaction force doesn't equal a unit increase in CoF.
This relationship starts to get interesting when you start to get into the understanding of weight transfer on vehicle dynamics.
To further demonstrate this effect with some numbers, i did some hand calculations (below). With a theoretical 75% weight transfer, there is as much as a 10% reduction in cornering force! (Zero weight transfer is impossible, but useful to help explain this concept.)
Now, exactly how much the CoF decreases with increasing vertical load falls into the realm of 'tyre load sensitivity'.
The concept of tyre load sensitivity is a method of communicating the sensitivity of the tyre to changes in vertical load - in the context of how much frictional force (lateral and longitudinal) it can generate. A tyre with less load sensitivity will see a smaller reduction of frictional force than a tyre with more load sensitivity. The former is of course much more desirable!
As a side note, the slip angle at which a tyre generates it's peak grip also increases as you increase vertical load, something else to consider.
Much effort is put into keeping weight transfer and roll to a minimum in race car design; maximising track width and minimising CoG height are key for weight transfer, while optimising suspension geometry and maximising roll stiffness help to keep body roll to a minimum and ensure the available contact patch is used to the fullest effect.
Phenomenon like this reinforce how motorsport and automotive engineering draw from such broad areas of science and why it's a great learning platform for engineering and physics!