I think of it this way . . . .
The heavier the aircraft, the higher its minimum drag speed (ie min clean speed).
Therefore, for a given IAS - say, a standard 300 kt descent - the heavier the aircraft, and the lesser the margin between its min drag speed and descent speed. So the aircraft is operating closer to its best glide IAS, and consequently its RoD will be closer to its minimum, which logically must occur at best glide IAS.