Mariner9 No offence mate but I'm glad to see you are not a flying instructor. Weight cannot change since it is Mass x Acceleration Due to Gravity. Neither of these can change.
Lift is generated to equal or exceed weight - thus geese go up or remain at same altitude.
The change in gravity due to the distance from COM is negligble. It really is worth ignoring in this instance. Imagine the aircarft flying at 100'.
In the grand scheme of things the parcel of air and geese inside the aircraft does not change in mass and thus weight. All the geese are doing is expending energy to move around the aircraft just as a human would walking around the aircraft.