Going right back to basics - Since the helicopter 'weighs' the same, it takes the same amount of lift force to hold the helicopter at 1 foot above the ground as it does at 100 feet above the ground at the same atmospheric conditions. It also takes the same amount of lift to hold the helicopter at 10 feet above the ground whether you're at sea level or 10,000' above sea level.
The power required to overcome the drag of the blades and produce the lift is the thing that changes.