Conventional pneumatic tires do not behave as classical friction theory would suggest. Friction theory says that the maximum horizontal force developed should be proportional to the vertical load on the tire. In practice the maximum horizontal force Fy that can be generated is proportional, roughly, to the vertical load Fz raised to the power of somewhere between 0.7 & 0.9, typically .

They typically develop this maximum lateral force at a slip angle of 6-8 degrees, although this angle increases as the vertical load on the tire increases.

As an example, here is data extracted from Milliken & Milliken's Race Car Vehicle Dynamics, figure 2.9

Vertical load Fy/Fz Slip Angle
(lbf) max degrees
900 1.10 5.6
1350 1.08 6.0
1800 0.97 6.7

The same sensitivity is typically seen in the longitudinal forces, & combined lateral & longitudinal slip.

In a Pacejka tire model the lateral load sensitivity is defined by parameters A9 & A12.