E1453,
That is exactley the point. IF you varied the speed to maintain a particular angle of attack (for example, that for max L/D) with changes in weight, your descent angle (and therefore distance) would remain the same.
We don't, however, routinley descend jet aeroplanes at optimum speed (and therefore optimum AOA) for the simple reasons of wishing to get there asap, and are usually restricted to 250kts below FL100. Distance therfore varies with weight AT A PARTICULAR DESCENT SPEED.
Why does it increase with increased weight? Think of it this way. You get the longest glide from flying max L/D, which will be a constant AOA. The speed to achieve this INCREASES with INCREASED weight. If we descend at a higher speed (which is almost always the case) we descend at a steeper angle.
If our aircraft is light, MAX L/D might be at 180 kts. If we descend at 280kts, we are flying 100kts above max L/D, and therefore descending much more steeply. If our aircraft is heavy, max L/D might be at 220kts. Our 280kt descent is now only 60kts over max L/D, and therefore shallower than in the case of the lighter aircraft.
Rember the oposite will be true at slower speeds. Fly the light aircraft at 180kts (Right on max L/D) and she'll glide forever. Fly the heavy one at 180kts (40 kts BELOW max L/D) and it'll drop like a rock.
Hope this helps.