A couple of things that could help.

1. Install Weapon for FSX using the "Run as administrator" option - right click on the installer (csw001_1000.exe) and select "Run as administrator" from the list that pops up.
2. Run the Loader using the "Run as administrator" option, then add Weapons to the aircraft of your choosing.
3. You might need to run FSX using the "Run as administrator" as well. This depends on where you installed FSX. Like if you installed FSX in the default location (C:\Program Files (x86)\etc.), which is not recommended because of the strict control the Operating System holds over that location.

Try some, or all, of these should get it working for you.