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Personally, I've played heavy mouthpieces and never really noticed much of a difference. Once I A/B'd a regular and heavy version of the same mouthpiece. There was no difference until I was really laying into it, to the point that it was unmusical.

The best line I ever heard concerning the use of heavy mouthpieces basically said "They help with players who are blowing with to much pressure and not enough air flow."

I compared the PT50 and the PT50+ when buying my CC-tuba.
I DID notice a difference in tone color, plus the notes seemed to slot easier on the 50+. However, this easier slotting comes with a very defined sound, making it seemingly harder to make those slight changes in tone colour that may benefit a solo situation.
I ended up buying the 50+, and I´m VERY fond of it.
(I don´t do that much solo work, and for my level of playing it´s best to go the safe way rather than messing with sound color)
Then again, the difference in weight will be expressed in grams, not kilograms.