I haven't done a complete survey, but I believe it also affects the damage. Powers that deal 1[W] or x[W] damage all have the Weapon keyword.
FWIW, Corrosive Ruin and Electrified Lash (and possibly others, I stopped looking after finding a couple) are Swordmage Implement powers that use [W] to determine damage. (Which leads to interesting problems when using no implement or a non-blade implement.)