Regarding the component editor,If you select a joint in the component editor you can see all vertices that have a weight value assigned to that joint and the amount of weight each vert has.
The theory is this ..the weight of the skin cluster for any given joint must add up to 1 and must always add up to 1 so the verts in the cluster around it get a weight assigned that the total should add up to 1 ,an example of this would be 3 verts could have 0.333 each or 4 verts will have 0.25 each or they could have 0.1 ,0.4 and 0.3 and 0.2 which also adds up to 1.
If you assign a weight of 1.0 to any vertice then that is the only vert that will be affected by that joint,but here lies the probelm be cause every vertices must have some weight from one joint or another if you add weight to a vert it will remove a proportionate amount from the others so it still adds up to 1 and likewise if you remove weight from a vert it must add more weight to the others so it's a balancing act to get the right amount of verts with right ammount of weight for each joint.

This is easiest to achieve by getting it close what you need using artisan painting the weight but is easier to fine tune in the component editor,adding or subtracting little values to each vert as needed.

So Like Elephantinc said check all the joints in the arm to make sure none of them have any influence over the body because evn if a finger joint had 0.01 it will still influence and pull..

Hope this explains it a little and helps you sort out your problem.