Weight paint only works on some objects

Sorry, I’m aware there are quite a few topics about weight paint not working, but I can’t figure this out.

The weight paint brush works fine on some objects, while on others it doesn’t at all:

Here’s my file:

Help once more.blend (2.8 MB)

Haven’t looked at the file, but looking at your coat, it’s in vertex mode, and no visible vertices are selected.

Still doesn’t work when I select vertices.

It worked after I applied the mirror modifier.