The A4 weight paper would result in a design similar to the fast flying and relatively pitch unstable paper airplane walkalong glider. Regular paper has too high a mass per unit area. I'd recommend waxed tissue paper (available at florist shops) and the design improvements incorporated in the indoor paper airplane walkalong glider design.

Here's a just published instructable on a paper airplane walkalong glider:
http://www.instructables.com/id/Paper_Airplane_Walkalong_Glider/

Thank you for your enthusiasm. I guess what you mean is the X-surfer or Z-surfer design? Bear in mind the flying wing designs require quite a bit of continual ballast adjustment, like before each flight. Until I pull together the instructable, please see the directions for the X-surfer, Z-surferand jumbo flying wing walkalong gliders.