How does planet size affect weather?

For simplicity assume hypothetically we make multiple copies of earth: XS, S, M, L, XL. The only difference between them is their size (radius), everything else is the same. S is half the size of earth, M is earth, L is twice the size of earth. XS is a quarter of the size of earth (the moon?), XL is four times the size of earth.

Will the fact these planets are different sizes noticeably alter the weather? How and why? Is gravity the biggest factor, or the size of the continents, the distance the wind has to travel, the height of the mountains, depth of the sea, the amount of energy absorbed from the sun... etc, etc, etc? Will L have more extreme weather and S have milder weather than M?

Bonus question: if each planet has the same gravity, because we like gravity as it is; how seriously would this change the previous question?

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How does planet size affect weather?

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