Actually, it would apply even at the same speed.
The reason is that a heavier aircraft actually has a smaller descent angle than a lighter one, even at the same speed. Consider the following.
Same aircraft, one weighs 50klbs, one 100klbs. Both wish to descend at 300kts, both have engines at idle and same config (this is emergency descent type numbers, but it works the same everywhere). In both cases the nose is pushed down until the aircraft stabilises at the desired speed. Since the plane needs gravity to provide thrust, the lighter plane needs to dive more to make the weight pull more along the flight path. So lighter aircraft actually will descend faster (in terms of ROD) than heavier ones, even at the same weight. It's all a result of having a limiting speed to obey.
Now, with a higher RoD and the same airspeed, you can start the descent later. So lighter aircraft start to descend later, and follow a steeper profile.
As an alternative: which is easier to keep to a speed limit driving down a hill - an empty truck, or a full one? Obviously, the empty one, because the heavier one wants to go faster. If you had bad (or no) brakes, the heavy truck couldn't go straight down the hill, but the light truck might be able to. Same ideas at work, more or less.