'Bone weights' is a misleading term when you don't mention the vertices, but speak only about bones.
The term 'weight' in this context doesn't mean anything physical, it is a term about the relation between two or more bones and a vertex.
A model with bones with each vertex connected to one bone only(!) has no 'bone weight', a model with the vertex where at least two bones are connected to that vertex and influence the position of the vertex got 'bone weight'.
The influence of the bones can be half and half, but it can be 10% to 90%, or any other ratio, this is meant by weight, the balance of their influence to the connected vertex.