Gravity is not a factor here. A ground path is tied to the rotation of the earth's surface and an air path is mildly associated with the movements of the atmosphere. If observed from above the great circle path is a straight line at any one instant but the air path is not tied strictly to the ground path. From an outside observers vantage point the ground path is an arch because the turning earth is not allowing you to drive a straight line. It may be compared to landing an airplane in a cross wind, you point the plane on a vector slightly away from your destination because the wind alters your flight path to match the ground target.
