Here’s how you should have done it…
- Select the mesh, go to Weight Paint and paint some patterns to the vertex group so I can see if they stay unchanged.
- Delete the middle bone vertex group.*
- In Object mode select the armature.
- In Edit mode subdivide the middle bone. Put armature back into Pose mode.
- Select object and put it in weight paint mode.
- Select middle 2 bones (or any bones you want to redo the vertex groups / weighting on).
- Key W > Assign Automatic From Bones.
Assign Automatic From Bones from this special menu will create new vertex groups for selected bones if none exist, change the vertices assigned to the vertex groups for those selected bones if they already do exist, and then set the weighting for those selected bones only. It doesn’t change anything in unselected bones/groups/weighting like the “parenting” shortcut Ctrl P does.
*Notice if you didn’t delete the middle bone vertex group step 2 this would still work since one of the “new” bones was left with the same name after subdividing. The group would just get its vertex assignments changed before weighting to the new bone of the same name.
Ctrl-P Armature Deform menus do any or all of the following. Parents the mesh object to the armature object and adds an Armature modifier to that object, sets up vertex groups named after bones, assigns vertices to the groups, weights the vertices in those groups. All bones every time as you found out. (I think it will stack up multiple armature modifiers too if you do this more than once -unless this behavior has recently been changed. Another pitfall for the uninformed).
Key W special menu Assign Auto From Bones automates the vertex groups creation, vertex assignment, and weighting for selected bones on an object already parented to the armature and has an Armature modifier already set up for it.
Confusing? Yes, unless you know how to do it all manually as norvman suggests. That should be a requirement before being allowed to use the automation shortcuts. They are a menace to new users when things go wrong.
Edit: Well, obscure features in hidden menus can catch out gurus too, no doubt.