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I'd like to know the answer to this also. For example, when I turn in a quest, does that exp get divided between both my skillbars and weapons, or just my current one?
I believe XP only applies to the item you've equipped. So, if you want to level your secondary weapon, but not necessarily use it, just swap out the weapons right before you turn in quests.
This also works for skill lines. Whatever is on your skill line is what is gaining experience whether you use it or not.