The design parameter that influences compressibility effects on lift is the Critical Mach number (Mcr).
This is the free stream Mach number when sonic conditions (M = 1) is reached at some point on the airfoil surface
The figure illustrates the same airfoil, at the same angle of attack at different free stream Mach numbers leading to the definition of the critical Mach number
The critical Mach number can be obtained through the curve for the minimum pressure coefficient as a function of Mach number. It can be determined through the intersection of the two equations
The lift coefficient correction for compressibility is
The figure on the left illustrates that
If you plan to fly at high free stream Mach number, you airfoil should be thin to
(a) increase your critical Mach number as this will keep your drag rise small
This will also result in lower minimum pressure - therefore you lift coefficient will decrease
Note that the minimum pressure coefficient on thick airfoil is high, this means that the velocity is also correspondingly high. Therefore the critical Mach number is reached for lower value of the free stream Mach number