Looking at your final question, it's important to make sure one thing is clear: a bigger cross-section (i.e. cylinder) will always twist less than a smaller one.
Yes, the outermost fiber of the cross-section will be rotated more than internal fibers, but the outermost fiber of a large cross-section will rotate less than the outermost fiber of a small cross-section. And therefore obviously the inner fiber of the large cross-section at a distance from the center equal to the smaller cross-section's radius will rotate even less.
That's because the rotation is proportional to the stress on each fiber of the cross-section. The stress is a reaction to the torsion, so Newton's Third Law tells us that the resultant "inner torsion" created by the stress must be equal to the external torsion. This inner torsion is equal to the product of the stress at a given point by its distance from the center, integrated over the entire cross-section. A larger cross-section can distribute that "inner torsion" over a larger area, so the resultant stress (and therefore deformation, by Hooke's Law) is lower than for a smaller cross-section.
As for why the outermost fibers deform more than the inner ones, there are a few ways to think about it:
We just assume it does. This is similar to the assumptions of Euler-Bernoulli Beam Theory, one of which is that sections that are parallel remain parallel under bending. Likewise, we assume that cross-sections under torsion behave as if suffering a solid-body rotation, with the relationships between all points within the cross-section being maintained. In a cylinder, this naturally implies that the more distant fibers must suffer more deformations: a point near the center barely has to move to rotate 1°, while one at the edge must move a lot more.
Obviously, this isn't a blind assumption: experimental data shows this is very close to the truth.
If you think of rotations in terms of angles, it just kind of makes sense. As described above, if you are rotating the whole cross-section by a certain angle, of course the outer fibers will be more deformed. The only other option would be to say that the angle of rotation isn't equal across the cross-section: i.e. that instead of all fibers rotating 1° and therefore having different deformations, that they have equal deformations and therefore different rotations.
Again, a good reason to say this isn't the case is because experimental data tells us it isn't. It would also lead to weird questions like "how to interpret the deformation at the center?"