When you bind bones, you're saying that the vertices' current positions are bound to the bones' current transforms. This is often called the "bind pose". Afterward, when you move the bone, it affects the vertices based on the weights. This is the whole reason to use weights: because you want vertices to be affected by bones.
After you bind but before you move any bones, you can set the weights however you want and the vertices won't move. Once you move a bone from the bind pose to some other pose, then the vertices that have > 0 weight for that bone will move. If you then change the weight for that bone to zero, the vertices will move back to where they were in the bind pose (assuming you haven't moved other bones).
The workflow is generally to bind your bones and then set your weights. You can use animate mode to manipulate the bones to make sure the vertices move like you want without messing up your pose in setup mode. You can even edit the weights in animate mode (for convenience, you are actually changing the setup mode weights, weights aren't keyable) so they move like you need as you manipulate bones. It's not common to bind, then move bones in setup mode, then adjust weights.
