New Bloke,
Let me pose this scenario. You have a vat that ’weighs in’ at 50 kg, sitting on a set of scales. You add 100 litres of water to the vat causing the scales to now read 150 kg. You float a 10 kg block of timber in the vat. Will the scales now read 150kg or 160 kg or somewhere in between? Of course they will reflect the full increase of 10 kg because the fluid is now supporting the block!
A plane load of geese is sitting on a weighing device on the ramp. The geese are perched. If the geese suddenly take to the wing, inside the aircraft, what change will the scales register. None, because the air within the cabin is now supporting the geese. The mass of the air and the geese is still supported by the aircraft structure! It makes no difference if the fluid + solid is water/timber or air/geese. The combined mass of the fluid and solid is unchanged. The scales are simply measuring a bunch of molecules and are unable to determine the actions/reactions of those molecules.
Hope this helps.