If she's not equipping what you trade to her , then she's decided her default gear is better. And enchants won't change that either it has to simply have a better base stat than what she's already using.
http://www.uesp.net/wiki/Skyrim:Illia
Sometimes you have to be careful what you let them carry if you don't want them fighting a certain way , but some of the companions seem to be "smarter" than othersEssentially if she were to equip the best plate armor and a big 2hander , she would behave differently than what you're used to.One thing is if ou dismiss her and go get her again , she'll be in her default gear , you can change this by taking a piece of the gear from her inventory and trading it back to her. This usually makes her equip everything she equipped before.