I think the opening statement is untrue.
A heavier aircraft will not always have a lower ROD, though it may be true in some circumstances.
This can be proved with a simple thought experiment.
If heavier was always lower ROD, then all you have to do is keep adding weight, and eventually it will stop descending.
Since this is obvious bollocks, then the statement is false.
Apologies DM, you got there before me
