Help for a Rigging problem!

After trying to rig this model,when moved the neck bone part doesn’t seem to be able to keep all the components of the mesh as a whole part.The parts of the mesh which are separate from the main mesh (eyes and teeth) don’t keep up with the main mesh even after i made the influence to be 100%. But to that problem, the lower bone that includes the arms as well as the head bends nicely and has no problem! I would like to see the same effect, but without the hands included. Is it possible to be managed like that? This is the image -