That's not quite accurate. Mass is part of the recipe for sure. What we are trying to do is transfer vibrational energy from the tube to the weight. However if we just consider mass with no damping - in other words we just use a high density, hard mass - the energy just keeps bouncing around. In fact if you keep increasing the mass at some point it becomes a pretty efficient reflector of the energy coming from the tube.
If you add a soft, squishy component to this mix the energy can be dissipated into that squishy stuff. Thought the actual intent of the vinyl on the lead rings is simply to contain the lead inside and protect the glass flask it is designed to rest upon, it happens that it's also quite a lossy material. We know the flask weights are kind of hard to acquire, and as an alternative PJ cooked up a weight that was composed of a few big steel washers of a total mass similar to the lead, with some silicone o-rings in between them for damping. Though it seemed like it should work very well, the lead and vinyl turned out to work much better.