Over the years the power of the vice president has varied widely. why

The vice president has zero power unless the president is incapacitated or the senate is tied or there is a join session of congress ( and here the role is more or less ceremonial). Anything beyond that is a matter of what the president chooses to delegate to him and his power of persuasiveness. Obviously, some presidents have delegated more than others and some vice presidents are more persuasive. A president could choose to rely heavily on the vp as Bush did with Cheney, or he could never see him or speak to him again after the elections - basically tell him to go home and they will call if they need him.