The Aedra, or the Nine Divines (now eight and one), expended themselves creating the mortal realms, according to lore. As such, they (rather ironically) can't interact with the mortal realms like the 16 (Now 15 that Jyggalag is dead?) were the 16 divinites that chose not to invest in the mortal realms, and created their planes of oblivion on which to resides. Basically, the Aedra are akin to the Daedra, it's just their position in the creation tale that's different.
So while you could consider Iron, Steel, Mithril, Dwarven, Glass, etc. as Aedric weapons, they can't manifest themselves into objects like the Daedric Princes can.