My archer never moved on the login screen either, and he has a bow. I don't even pay attention to it though.
Tray take off your fashion weapon. With my seek is the same. Sometime its move sometime no. EDIT: I just test it. With fashion weapon not move, but after i remove it, ini start move.
If it's the log in animation that isn't moving i believe it's because you need to have a bow equipped, not a crossbow or slingshot...