# Why is the polar diagram of an airplane depended on weight?

Can anybody answer this question? Although aviation-related, it is in fact a fluid mechanics problem:

So far I got only a lot of unsatisfying answers. Maybe here are experts on fluid mechanics.

For my understanding the polar-curve is a property of geometry only. It provides a $c_{lift}$ and a $c_{descend}$. Given those coefficients, the speed of a glider can be calculated by simple math, since force in direction and perpendicular to air flow is calculated by $F_i=c_i \cdot \rho \cdot v²$.

Even if that is not true because of non-linearities of whatever reason, I always imagine the aircraft to be tested in a wind channel of given air-speed with a given angle of attack: in that case (I assume) the flow of air and associated forces cannot be different from the real case. But then weight cannot be relevant. Of course different weights give rise to different velocity, but then this can be explained fully based on the polar diagram.

So why is the polar diagram depended on weight?