What are the circular discs people use on components?

Are you referring to the Combak tuning disks that were popular back in the 80s and 90s (and for all I know, today)?  They were gold-colored circular discs.  They did not damp things, but supposedly tuned resonances to a different frequency.

Most people use the door stoppers not for any "resonance" damping, but merely (as John Darko showed in many of his YouTube videos from two years ago) to hold lightweight components like streamers and DACs in place such that the weight of the cables doesn't pull them off the shelf or hold them up at a flaky angle.  Yeah, the weight would likely lower the frequency of any resonances, but your mileage may vary on that. They are a cheap fix and don't look that bad. 

Interesting for sure. Does anyone have any advice as to the amount of weight one should use? I assume it’s more for heavy amplifiers and less for lighter components  

If you've got circular ring above your component, then you're probably not in this world anymore.