When the drawer is pulled out it raises the weight by the string and pulley.
When the drawer handle is let go the weight goes down due to gravity and the drawer returns to its normal place. This is a great idea if it is a drawer you always use and its handy if you have your hands full and need to grab something and dash.
Cork, or rubber and such could be put in place to dampen the impact when the drawer returns to its spot.
I would suggest trying different weights until you get one that is quiet and does the job with ease.
If your drawer runs on wooden runners then you can use candle wax to ease the ride. Just grab a house candle that you have for power cuts and camping and rub that along the wood runners.
This will make the drawer run smoothly and make it quieter.
Experiment, enjoy, have fun, you will get the set up you desire with practice, patience, experiment and effort.
All the best from
James M Sandbrook.
27th of April, 2021.