I'm trying to rig a character but I have problems with the belt and straps of the bag. Somehow the automatic weight paint (?) does not work properly. I did join the meshes of the character and accessories. I tried rigify (prefered option) and some really basic self made rig. As one solution, I can extrude the belt and straps from the character mesh with the knife tool. That would be fine and it should be working but that's not my prefered workflow. Also even if it works right now, I'm not sure if I would add some accessories in the future for which it will not work. How do I fix my problem? By the way, I do have the problem even without the subdivison modifier.
Animated mesh with self made rig:
Close up of my problem: