Mesh does't move with armature I have two different mesh (head and beard) on one bone and they don't move together. I have weight painted them, set parent (to bone or other meshes).
Image below shows how should look like mesh:



And how it looks when head (bone) is turned:



[Link to blend file]
You have to remove the weight the neck has on the head and the beard.

Because, the beard is weighted on neck, so it influences when you move the head. 
Then you will notice the head, most specifically the chin is also weighted on the neck which makes it look like it's shrinking a little bit when you turn the head sideways, so you have to subtract the weight from that as well.