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If there are different rates for different Spheres, just put them in categories.

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Not that I can answer, but I've found many sources that say Prism and Pale Spheres grow slower, and conflicting sources that say sphere growth is dependent on in-game or real time, but in both cases growth rate is unclear. :P
From Bulbapedia:

"To get larger Spheres, they can be combined by burying more than one of the same color Sphere in the same spot. When combined, the size of the resulting Sphere is determined by the following formula:

X + (a⁄5+1) + (b⁄5+1) + (c⁄5+1)...
Unless the buried Sphere has grown at least once since a Sphere was added (or grown without a Sphere being added), in which case the formula is:

B + X + (a⁄5+1) + (b⁄5+1) + (c⁄5+1)...
Where B is the size of a grown buried Sphere, X is the size of the otherwise largest Sphere buried, and a, b, c, and so on are the sizes of the other Spheres. All non-integer values are rounded down before the adding. In the event of a tie for the largest size, the largest Sphere size is used both as X and one of the other lowercase variables. For instance, burying a Prism Sphere 15, a Prism Sphere 12, a Prism Sphere 7, and two Prism Sphere 1s produces a Prism Sphere 22. Burying a Blue Sphere 15, Blue Sphere 3, Blue Sphere 22, on top of a Blue Sphere 3 that has grown by 2 yields a Blue Sphere 32."

Hope that helps!
The question asks for how fast spheres grow by themselves, not what happens when 2 spheres are combined.
Red, Green, and Blue Spheres grow either 3 or 4 sizes daily. Pale and Prism Spheres grow either 1 or 2 sizes daily. We currently don't know what the chances of each increase are.
https://bulbapedia.bulbagarden.net/wiki/Sphere#Growing_Spheres

Is this enough for an answer?

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Buried Spheres grow naturally over time, at a rate depending on their color:

Prism and Pale: 1 to 2 sizes per day
Red and Blue: 3 to 6 sizes per day
Green: 5 to 9 sizes per day

Each possible growth size is equally likely.

Sphere | Growing Spheres (Bulbapedia)

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