Fine hairs have a diameter of around 40-50 microns. Medium hairs (average) have a diameter closer to 100 microns, but most hairs of any diameter have a cuticle that is about 4 microns thick. Fine hairs are about 35% cuticle and medium hairs are closer to 15% cuticle.
The cuticle doesn’t play much role in perming or relaxing—that takes place in the cortex of the hair, but this is one reason why perms for fine hair can be more difficult: there is less material (cortex) to be relaxed or permed relative to that which is not alterable by the chemical treatment (cuticle).
Use relaxers and perms for fine hair with caution—it will require a potentially more damaging process to dramatically change the shape of your hair, and its small diameter gives it less buffer from the environment once it is chemically altered.