The rule is valid when using the same camera, with weight-increasing appendices - you get an two extra stops out of a F3 when using it with the motor, powered off, or one stop extra by using the eight- rather than four-battery holder on the F4. But it is not true across different cameras - the ratio between static and moving mass and the timing of moving components do not depend on total weight.
Most heavy cameras also have increased moving mass - and the balance may shift towards the latter, making them less suitable for long handheld exposures. There have been ultra heavy cameras with horrible damping (e.g. the Pentax 6x7) and light cameras with excellent damping (e.g. Pentax MX), even from the same maker. And then there is the whole matter of timing (for example, the Mamiya RB67 kicked like a mule, but only after its shutter closed).
And on top of that there are manual shake issues - whose response to weight will also depend on your physical condition (and underlying diseases)...