Her robes are hooded so when you give her something to wear on her head she will often equip it. I have seen her switch back on forth on hats/hooded robes. If you want her to keep her robes unequipped, give her an actual helmet, assuming you aren't on pc and can't just remove/equip item on her. If you give her a helmet gauntlets and boots she will wear those and get a wee bit of armor and gain the benefit of enchantments, at least certain types, but her torso will remain bare and you can continue to admire her figure....
I like to make her a balltemage and give her a weapon. Then she will bomb stuff with spells until her magicka is low and if anything is still standing she will whack 'em with her sword. You can really stand back and let her do all the work most of the time.