Hello,
I have read your stackexchange entry and watched your videos. I am not sure why you exactly experience these problems, but I guess there is a problem with the weighting of the bones or maybe the manuelbastioni lab is confused wether it should use ik or fk rigging. I never used the clothes weaver addon and I also dont own it, but it seems like it wasn't parented properly to the rig. Maybe I could look into you .blend file and try a few things? I do have the manuelbastioni addon, so I could maybe help you with that. I would need the .blend and your bvh file for that. Maybe you could send me a link to it? I never had such an issue with an bvh file, but maybe we can fix it :)
Greetings,
Jasmin