When the helicopter is not running and sitting on the floor of the box, all the force, or potential energy, is on the floor of the box and being read by the scales.
When the aircraft is hovered the air is being forced down to the floor then out to the walls of the box and up to the roof to be recirculated. It would make sense to me to say that now some of this force, or energy, is being aplied sideways to the walls of the box and therefore would not bear pressure down on the scales thus the scales would read lighter in the hover.
Now though, what effect, if any, would changing the size of the box so that now non of the sideways air movement ever reaches the sides of the box?
Now my head hurts.