Both weight and larger grips are intended to assist removing as much wrist action as possible from the stroke. The higher weight allows a more controlled tempo on all reasonable putting distances and still achieve the same distance. I didn't go larger than the Cameron mid-size grip, but I'm stuck on the SC mass. Anything else no longer feels easy to control at a lighter weight. You might find distance control easier with the heavier SC on longer strokes since you don't have to move the pendulum as far. Still need to spend 2-3 times longer practicing with a putter than driver since you take 2-3 times more strokes with a putter.

I feel like I don't have to work as hard on longer putts with a heavier putter. Of course, it depends on the green speeds you usually play on.

If you feel most comfortable with the putter you have, I say stick with it. Don't get me wrong, I love that "new club smell" as much as the next person. But if it's not broke, don't fix it. Last thing I think I would change in my bag is my current Scotty, even for a new one.

I play a heavy SC it's a Big Sur S cut down to 34 inches head weight's in over 500 grams heavier putters to me help me control things better since I am swinging slower I swing smoother as well has really helped me personally become a better putter

Like said above you use less of the small muscles but in my case when I use a heavier putter my speed control goes down the drain.

My suggestion go roll some vs. your current gamer and ensure you won't have issues with speed.

George - Super Stroke grips are bigger but aren't necessarily heavier.
I have a loose Baby T and a loose SS 3.0; hopefully, I can get an accurate weight to you.