For some reason the starting weapons on some champions are not tradeable, just as you can't remove and trade their clothes. I personally hope this is something stardock look into. I wanted to take a cool looking staff off of one of my champions, it was green and called the "queens staff" so naturally I wanted to give it to my factions queen. Sadly the staff didn't show in the menu.
As for the clothes we should also be able to remove these. One of my Sov's sons came of age wearing these bright white shoes and a goofy hat... I have to admit I was so ashamed of him I left him in my home city while his more fashion minded sisters went off to strike fear into the hearts of my enemys. This issue is also compounded by the fact we are stuck with the unit cards the champions arrive with. Even if you make your champion look hard as nails decked out in magic armor their unit card will show them as the beret wearing wimp they really are.
Also they really need to look into fact hooded robes remove hair from female champions... so when you add armor to a robed female they are left bald. Perhaps Stardock could add a system where hooded items also have data for a hair model that gets added in when the hooded robe is removed or replaced by better equipment.
We should be able to buy the base clothes and "wigs" from the city store.