What is the effect of flying height on helicopter fuel consumption?
The lift equation shows that as air density decreases, as it does with altitude, in order to maintain lift, the speed of the blades must increase or, the coefficient of lift (CL) must increase.  Since the characteristics of the blades do not change, in order to increase the CL, the angle of attack must be increased.  

Increasing either of these increases drag so, in order to prevent the blades from slowing down, the engine must produce more power to counteract the drag. 

Most helicopters use constant speed rotors so in practice, the angle of attack (the pitch of the blades) is the only variable.  In order to maintain speed of the blades, the pilot, or a throttle governor, must increase power from the engine.

Therefore, a helicopter uses more fuel as it's altitude increases.