How does aircraft weight affect the glide performance?
The gliding slope, which equals $D/L$, does not change with weight. Hence, starting from a given height $h$, the longest gliding distance will be $d = h \cdot max(L/D) = h \cdot max(C_L/C_D)$, i.e., independent of weight.

However, the gliding speed, and, consequently, the gliding time, do change with weight, and significantly. If $C_{L,max}$ is the lift coefficient when $C_L/C_D$ is maximal, the gliding speed at best slope, $\bar{V}$, is obtained from $W = (1/2) \cdot rho \cdot \bar{V}^2 \cdot S_{ref} \cdot  C_{L,max}$.