Take a DC-9-41. In a speedbook I have handy I find a maximum listed weight of 52t and a minimum weight of 30 t.
Doing a bit of algebra, I find that the rate of descent is proportional to the drag (D) through the mass (m) of the aircraft. The drag will of course in turn depend on the mass, D(m).
Thus, the difference in descent rate, heavy aircraft descending faster being the positive, can be described by
V/S difference = D(52)/52 - D(30)/30 = ( 30*D(52)-52*D(30) ) / (52*30)
In other words, if
30*D(52)-52*D(30) > 0, the heavy aircraft will descend faster.
30*D(52) > 52 * D(30)
30/52 * D(52) > D(30) <=> 57% > D(30) / D(52)
Then the question boils down to if the drag at 30 tons is less than 57% of the drag at 52 tons at the given airspeed. If that is true, the heavy aircraft will descend faster.
I find it highly unlikely.
Cheers,
Fred