If you start a new character, will you get the preorder weapons again, or is it locked to your first character only?
Solution 1:
I own the PS3 collector's edition with the additional items provided by the pre order, having said that I have 3 characters and they all had the pre order items available when they were created. I hope this helps you even though I know it's not the PC version.
EDIT: As confirmed by @TonySniper mentioned in the comment below, this does apply to PC as well.