Each skill or spell has its own Attack/Defense/Support levels that increase randomly in battle when used in the corresponding role, i.e. a skill will level up in Attack when the character is in Attack, Support when in Support and Defense when in Defense.
What those levels do is, I think, improve the efficiency of the tech or spell in this particular role.
Keep also in mind that a skill's efficiency is modified depending on the role (offensive skills do more damage in Attack, curative spells heal better in Support and shield skills block better in Defense).
So, I haven't much tested but I imagine an offensive skill with a high Support level but low Attack level will do as much, if not more, damage when used in Support, despite Support being basically less strong than Attack (that is, if the character himself has the same level in Attack and Support).
What those levels do is, I think, improve the efficiency of the tech or spell in this particular role.
Keep also in mind that a skill's efficiency is modified depending on the role (offensive skills do more damage in Attack, curative spells heal better in Support and shield skills block better in Defense).
So, I haven't much tested but I imagine an offensive skill with a high Support level but low Attack level will do as much, if not more, damage when used in Support, despite Support being basically less strong than Attack (that is, if the character himself has the same level in Attack and Support).