Aren't you guys forgetting Newton's Third Law? Every action has an equal and opposite reaction. If a 1 kg (9.81 Newton really) goose is flying then the air below it is being forced downwards by a force of 9.81 Newtons. This will have the effect of increasing the air pressure on the floor of the aircraft and decreasing the pressure on the roof by, guess what, 9.81 Newtons. So the aircraft will appear to weigh the same. This is what's known as a 'closed system' - it doesn't matter what you do inside it will maintain its weight.