Raely's extensive testing found out that this is spell-dependant, despit tooltips using the same note for all of them. In most cases, "weapon damage" is your weapon, rings, amulet, and arrows. But not always, as it seems NGD coded each spell individually instead of using a macro for these calculations.
One thing seems to be constant: Gems (in your weapon), and dexterity, never count for "weapon damage". This may have changed over time, though. All of the known information, especially on the Wiki, is very old, and was made pre-Warmasters update (though some of it was updated). We need people to volunteer for extensive re-testing so the Wiki can be pretty much rewritten with the new game logic. But seeing as how a new expansion is coming, there is probalby no point...