My experience with added weight on the mouthpiece involved a set of custom Curry mouthpieces. Adding a Monster Sleeve did make the sound darker by about 1 Bach cup letter (to me as a player and also to colleagues listening to the with/without combinations) while retaining the upper-register comfort of a shallower cup.
A player who sounds just fine on their normal weight mouthpiece and is happy has no reason to switch to or even try a heavier weight. They do do something, for some players positive, but I would warn against getting into the "how many grams is ideal?" kind of safari.
That would lead to madness.