For You as a Swiss guy You will understand next, I will try to keep it as simple as possible.
Driving uphill in a car requires energy. Driving the same car, but now with 4 people on board, requires much more energy. The more people in the car, the more energy needed. Going down, the heavy car will need using the brake much more often than the same, but lighter car.
Weight is "the engine" during descent, to keep the car rolling, the more weight, to more "power" You have. You cannot switch off the "weight engine".
So once two cars are on top of a mountain, the light one has much LESS (potential) energy stored than the same car, with 4 people in it.
But You cannot change the % of slope on a mountain, airplanes CAN change their descent angle.
Example: two identical airplanes, both at 10km of cruising altitude, one at max allowable weight, and the other one, as empty as possible, will have a enormous difference in energy state.
For a normal descent, both will fly at the same SPEED. But the heavy one needs to select a LESS STEEP descent angle, otherwise the excess energy will drive the plane into crazy dangerous speeds. OR it needs to pull the speed brakes (like the car), but that is highly uneconomic.
In the 747 I flew for 22 Years (all types), descent planning was done initially by looking at a simple table: The more WEIGHT You had, the MORE distance You needed to start the descent before destination, in order not to overshoot the destination.
By dusted memory, at a very light weight you needed about 110 Nm before destination, but when You were heavy, it would be 130 NM or so.
Remember, airliners use idle power during descents, so that is not a factor. Here again, weight is the engine that maintains flying speed.
Ik kept out wind influence, difference in gliding performance at different weights, I think those are NOT the factors, TS is looking for.
Modern airliners do the calculation of where would be the optimal TOD (Top Of Descent), that flight, electronically, but it also uses actual weight (together with things like forecasted winds) as the MAIN factors to determine that point.
Richard