The McCormack DNA1 was my first real high end amp. Inside the box was this cheesy looking pointy nut screw thing. The manual called it a grounding spike and said try something like a coin under the spike. Looked silly and the pathetic but I tried it and sure enough it did tighten things up a bit. This was back early 90's. So Steve McCormack was an early adopter in the area of vibration control.
That's really what is going on. Everything vibrates and mass tunes the vibrations. But not only mass. The same mass of lead, copper, iron, stainless steel, sugar, books, wood, carbon fiber, acrylic, will not sound the same.
The thing is, where this comes into play with us and the OP question, this whole mass matters question is but one of many the designers and manufacturers have long since taken into account. One may do it like Steve all deliberate, another may do it by total disregard as not worth the time/money/effort. Whatever. Doesn't matter. Point is from our point of view all that matters is the result. There's just way too many different variables to think its even remotely possible we could look at something as silly as design and think we are able to figure out what will make the difference and what will not. Which is why we have to go and listen.
But then, once we find the best by listening, then we use our knowledge of things like this to make it even better. Understanding not only mass matters, but stiffness, and damping- and those three are only the three that matter in the area of vibration control. Then there's the circuit design, which we generally have no control over (hardly anyone proficient enough to alter a circuit- note I said alter not merely upgrade parts quality in the same circuit which is a whole different thing). Then there's acoustics, and electricity. Which if you read mahgister he calls these his 3 embeddings. Whatever. Same general idea.
So even something as silly as "does amplifier weight matter?" turns out to have a serious side to it. Its just the silly aspect needs to be stomped to death, because its freaking rampant across the whole audiophile community. Everyone obsessed with arbitrary technical minutia like this when its a (near) total waste of time that could much better be spent listening and learning how this stuff actually sounds.