Blender Rig is really wonky

Forgive me if I’ve made any mistakes prior to encountering this problem, I’m still new to rigging.

After modeling a basic character for a project I’ve been working on, I applied a rig to my character with automatic weights.

I then proceeded to assign vertex groups to said character.

However, whenever I rotate any limb, it seems to scale the vertex group assigned to it.

Image 1: http://i.imgur.com/wseFGna.png

And whenever I move the bones, the mesh seems to be left behind.

Image 2: http://i.imgur.com/pSYoBna.png

Is there any way to stop this? I’m about to pull my damn hair out. Thanks in advance.