You have duplicate vertices in your mesh. When you attempted to parent the mesh to the rig, an error flashed on the bottom of the screen and you must not have noticed it:
99 times out of 100 this means You have duplicate vertices in your mesh. Blender's algorithm for automatically assigning weights will fail if the mesh isn't manifold, and this is the most common reason why a mesh won't be manifold. (See below for a definition of manifold.)
To fix this, using your first blend file as an example
Remove the existing attempt to parent
- Switch from Pose to Object mode. (Shortcut: Ctrl–Tab)
- Select the object
CommandoMesh
- Go to Object properties in the properties editor.
- In the Relations Tab remove
Rig
from the Parent field by clicking on the x.
- Go to Modifiers in the properties editor.
- Delete the Armature modifier.
- Go to Object Data properties in the properties editor.
- In the Vertex Groups panel, click the down arrow to bring up a menu.
- Select delete all groups.
Fix the duplicate vertices.
- Switch to Edit mode. (Shortcut: Tab)
- Make sure all vertices are selected by typing A
- Bring up the merge menu. (Shortcut: m)
- Select By Distance.
You should see another message appear on the bottom. Please pay attention to messages that appear there. It will tell you that you had 2442 duplicate vertices but they were removed.
- Now the parenting will work
- Switch to Object mode. (Shortcut: Tab)
- Shift-select
Rig
to add it to the selections.
- Parent
CommandoMesh
to Rig
. (Shortcut Ctrl–P and select With Automatic Weights.
There will now be no error message and the rig will move the mesh.
The Blender manual describes Manifold thusly:
Manifold meshes, also called ‘water-tight’ meshes, define a closed non-self-intersecting volume
Tip: The Info Window
Often we miss the information messages that appear on the bottom of the Blender window. When an operation fails, it's possible to open the Info editor window. You can find it in the Scripting Workspace or you can open it in any of your current panels using the drop down menu:
Scroll backward through it looking for the various info or error icons. Often they'll help you solve the problem, or at least make it easier to search for a solution online.