Isn't a birds wing shaped like an airfoil? Or perhaps more correctly stated, isn't an airfoil shaped like a birds wing? In which case after the bird has gained forward momentum is not some of the lift caused by the low pressure region developed on the top surface of the wing? I would aslo contend that a box with a rotating propeller on it would indeed weigh less as not all of the lift is developed by downward force. Some of the lift is developed by the low pressure created on the top of the prop. Generally speaking an airfoil does not produce lift via downward force but by developing a negative pressure above it's top surface.