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So ok, there is some classical interpretation of this: If we imagine our particles as little spinning charged spheres, then sure if they have more mass then they require less angular velocity to possess a given amount of spin angular momentum, and since they spin slower it seems intuitive that they should produce smaller magnetic moments.

However since we are in the quantum world this picture makes no sense since angular velocity for point particles makes no sense, so it does not seem right to imagine that protons "spin slower" than electrons (although they are composite so perhaps it is slightly more valid: say we are talking about muons then).

So in what way should one think about the mass dependence of magnetic moments if the "rate of spinning" is silly? Perhaps if someone would remind me how we derive magnetic moments from QED or something that would also help.