Prevent mixing of weights in a bone Both bones enabled

I'm trying to add a bone to deform the character, so I could easily make it look fat or skinny. The problem is that the other bones seem to be affecting the result, even thought they are not moved (their weight maps cause the unwanted deformation). You can notice the deformation in the right side of the first picture. Can you explain me why is this and how can I prevent this?

This character is for a video game.
You can delete what vertex group each individual vertex belongs to 

3D view Editor-->Edit mode-->(n) properties shelf-->vertex weights.



Imagine each vertex group = a muscle. 

The more vertex groups control a single vertex= the more muscles are connected to that vertex . 

So when you are trying to make the belly bigger with one muscle, the other muscles are still attached=you get uneven stretching.

And the muscle strength can only be changed manually in weight paint mode or by using the vertex weight modifier.