Why are the size and shape are different in edit and object mode? When I change the mode, the mesh looks different. Edit mode-skinny, object mode-fat. Before I made the skeleton, everything was fine.
Make sure that before you do automatic weigthing, that you apply the scaling to both your mesh model, and you rigifie armature  [CTRL + A]

once all scales are applied it shouldnt deform, i see this happen often with people who begin with this.