As I picture it, an aircraft that weighs (for example) 200 tons, has to be creating 200 tons of lift every single instant to stay aloft. To climb it needs to create more than 200 tons, to descend less than 200.
It does this due to the effect of the wing angle of attack coupled with the shape*, which when combined force 200 tons of air downward every single instant, thus winning the battle against gravity, which is trying to pull the aircraft down at 9.81m/s
at all times.
That's why work is being done even in straight and level flight.
Plus of course barging a plane shape's worth of air out the way, 'dragging' along a heap of air due to the boundary layer, creating all those wing vortices etc. Whole bunch of stuff going on when you get up close and personal with air at speed!
Same reason your arm aches - holding it out is actually resisting gravity which is trying to accelerate your arm downwards. Don't think there's a boundary layer or drag to consider here though.
*Ignoring body lift etc as it's easier to simply think of the wing as creating the lift.