It isn’t larger than the proton, if you are referring to Rutherfords experiments which showed the exact size of the nucleus.
It is true, however, that the particle’s mass is proportional to its spread. Quantum mechanics is more applicable, so to speak.
The Bohr radius, for instance, gives us an estimate of how far the electron can be away from a proton during the formation of the hydrogen atom. We could loosely say that the electron “spreads out” within a radius of this radius.
This is the formula:
a0=meca
I won’t bore you with the details of the other constants. But the point is that if we double the mass an electron but everything else remains the same, it will “spread out”, in a sphere that is eight times smaller.
Although this is a sketch and is intentionally vaguely stated, it is the general idea. Because their mass is smaller, smaller particles are more likely to spread out.