Aircraft Energy Question

[Rivet gun]

So we are considering an aircraft in straight and level (un accelerated) flight.

Looking at the problem from the aircraft's frame of refrence, we resolve the forces into vertical and horizonal components.

In the vertical direction, weight is balanced by lift but there is no vertical motion so no work is done or energy consumed in providing lift per se.

In the horizonal direction however a certain amount of drag is an inevitable consequence of generating lift. To maintain equilibrium drag must be balanced by thrust. Thrust comes from a propellor or jet which works by causing air to accelerate (i.e. it adds momentum to a mass of air). Adding momentum to air requires energy and the energy comes from burning fuel.