disco_air
By your theory, 404 Titan, if the birds all flew towards the back of the aircraft (lets assume they stay airborne), since the weight hasn't disappeared, does that mean the aircraft's CofG will move rearwards in flight, causing it to pitch up with all else being equal?
Yes the CofG will change as the birds become airborne compared to when they were perched but the weight will remain the same. That is the question that was originally asked. As I have previously alluded to the weight of the birds when airborne will be evenly distributed across the floor of the aircraft by the air. Therefore the CofG won’t change if the birds fly from the front of the aircraft to the rear as long as they don’t become grounded. If they walked to the front or rear then this is a different story.
Soulman
This contradicts what most of us have already concluded - since the aircraft and it's occupants are considered to be one system, the net force is zero.
No the question asked was what happens to the weight not the CofG. As has been shown weight doesn't change. CofG may change when the birds become airborne but the weight doesn't change. I might point out that even though the lift of the wing may change because the CofG changes the gross lifting force from the wing and tail plane would remain the same in steady level flight because of the varying lift forces produced by the tail plane to counteract the various CofG positions.