As you found: "you can seem to get it working somewhat?" This is that "somewhat". "Weapon mods" don't work with retextures that are not vanilla compatible or patched to work with specific mods.
In the case of (for example) "Weapon Retexture Project" (WRP) v1.95, the package has a "non-standard" folder structure. (Not an uncommon mistake by mod authors, so learn from this.) The game (to include most mod managers like NMM, MO, and FOMM) is expecting the top level folder of an archive package to be standardized; with folder names such as "Textures" or "Meshes" (etc.), or ESM/ESP/BSA files. It assumes they are being placed under the game "Data" folder. This example package starts with a "RLS" folder, which the game does not recognize, and so it places that as the "top level" under "Data". (Sometimes this is the author's name or initials, other times it's the mod name and version, but anything unexpected is treated the same way: as a new folder or file. Sometimes it's "Data" so you end up with "Data\Data" which is also unexpected.) Most likely when the files are "installed" but aren't found correctly, something similar to this is your problem. Unpack the mod archive (WRP in this instance) to some other location and then either rebuild the archive so the top level folders are "Textures" and "Meshes" (in other words, without the "RLS" folder from WRP at all), and then install with your mod manager, or manually drag those folders into the game "Data" folder.
The text file under the WRP "RLS" folder is a documentation file. If you want to keep similar in the package, just place it in the top level along with the "Meshes" and "Textures" folders. Recommend renaming such to "<mod_name>_ReadMe.txt" so you know which package they came from, and place them all in a "Docs" folder for easy access, but it's not a requirement. (Many authors act as if their mod's text file is the only one that might possibly exist in the same location or use the same common name (i.e. "Readme.txt"), so consequently only the last installed exists.)
The later versions of WRP correct this folder structure, but that breaks compatibility with older patches designed for v1.95 to work with other mods. So the first thing you have to do is ensure you know which version of WRP you have installed and what it is compatible with.
Edited by dubiousintent, 21 May 2020 - 12:34 PM.