Balancing a mutli-label dataset is a bit tricky, as a simple weighted sampling might even increase the imbalance, e.g. if the majority classes are often associated with the oversampled minority classes.
There are a few approaches, such as SCUMBLE, REMEDIAL 79, MLSOL 33, MLSMOTE etc.
I don’t know, what the current state of the art is, but I’m sure @rasbt would know.