There are several interpretations of what "double weighted" means. The one that makes most sense to me is this:
Double weighted is a state where the balance of a person is broken in such a way that the person cannot move effectively without taking a step (a fraction of the body is supporting all the bodyweight, so it's supporting "twice" the load it would naturally hold).
You may find this interesting:
The positions in your videos don't look double weighted to me.