I've looked at several answers to this question and none of the responses are giving me what I need.
Vertex groups are selected in the armature options, the vertex group names correspond to the bones I want them to be attached to, and I parented the armature to the mesh with the 'armature deform' option (I tried automatic weights and the result was even worse).
I would have thought that the vertex groups would be influenced 100% by the bones sharing the same name as the vertex group, and 0% by the bones that do not have the same name.
This is not what is happening, as can be seen here:
The 'base' bone influences the 'base' vertex group fine, but also influences the 'lid' vertex group -which I don't want. Furthermore, the lid vertex group looks like it is only 50% influenced by the lid bone, as shown here:
I know there is an obvious remedy to this, but it's one I don't like using. Weight painting is not precise and very fiddly.