And thus I’m not sure when using the equation for profile drag D = .5 rho Cd Vsq S that it is fair to say that the profile drag depends on weight because of a changing frontal area.
Not in reference to S, but induced drag is made up of elements of parasite, form and skin drag so it is probably technically correct to say that at higher AoA it isn't just the increase in CL that contributes to the additional drag but the larger surface area too.