In the classical boundary layer solutions the thickness and other values are dependant on Reynolds and Mach numbers at given abscissa. Take the simpler example of incompressible boundary layer: the Reynolds number can be augmented or diminushed independently (at last directly) of pressure. In fact the dependance on pressure is contained in boundary conditions given by inviscid flow.

The pressure affects the density and velocity of gas in my case(LPCVD), hence the Reynolds number changes.So I think one of the book i refered made a mistake.