I've been trying to add weapons to armor, using the copypasting method outlined in the CSwiki tutorial: http://cs.elderscrolls.com/constwiki/index.php/Making_New_Armor_Using_NifSkope , trying to use a copy of the Elven Shortsword (one set to BackWeapon, the other to Quiver) to paste them onto the back of my new armor, but for some reason it just stays flat at the armors feet.

Does anyone know what I can do to make this work?

It's because those are not rigged to any bones but attached to those PRN nodes rather. If you open a weapon NIF in NifSkope, you won't see an armature of bones and the weapon at its place but rather only the weapon somewhere in the center. And that's where it will stay, if you paste it over and parent it to an armature.

I don't know if this can be done using NifSkope alone, but I do know I can do it (and did) in Blender (or another modeling app) without much trouble. Well, as I can't remember anymore how I even got it imported in the first place it might not be that much without trouble, but still once you got it imported and parented to the armor's armature you only have to rig it to the bones of your armor, either using the Copy Bone Weights script or weight-painting it manually, or maybe even by just giving every vertex a weight of 1.0 to a bone of your choice (similar effect to the PRN attachment route). This depends on where on your armor the weapon is to be mounted and in which way, if it will bend or anything, etc. It will no longer be a weapon but a useless part of your armor just for looks, if everything went right.