QJB,
Not quite sure what you mean.
If Best L/D were the usual descent speed, a heavier aircraft would descend at a higher speed than a lighter one.
I guess the best way to put it is this- Best L/D speed increases as a function of weight. Fly faster OR slower than best L/D, and you will not glide as far.
I would think that a descent with an FMC cost index of zero would have the aircraft descending at very near best L/D, perhaps modified slightly for residual thrust. Would anyone like to clarify that?