I can't find any of the Weapon Nif. files in
C:\Program Files\Bethesda Softworks\Fallout 3\Data\meshes\Weapons

Why arent they there?

All the default meshes are packed in the Meshes.bsa file. You'll need to unpack them first before you can access any particular mesh. You can do that with FOMM.

They are packed in the BSA file. If you have FOMM you can unpack them by double clicking on one of them, like Fallout - Meshes. This will open it with FOMM, then you select the files you want, and click Extract. Just do this with as few as possible, as it takes longer to load the extra files not packed in the BSA. So if you were to unpack all the BSA's entirely, your game would be very slow compared to normal. But a few files here and there (I have like 25-100 unpacked at all times) won't hurt at all.