Suppose you have a plane that can hold two thousand pounds, and you decide to load it with over two thousand pounds of birds. If the birds fly in circles inside the plane, will it be able to take off? Does the plane weigh less if the birds are flying rather than sitting?
Here's a hint. Think about lift and weight, the two opposing vertical forces involved in flight. The birds support their weight in the air by flapping their wings and creating lift. As the wings push down on the air below them, the air pushes back up against them.
The air pressure below the bird ends up equaling the bird's weight. And the weight of the air under the bird's wings, instead of the weight of the bird, pushes against the plane's floor. The total force against the plane's floor is the same regardless of whether the bird is sitting or flying.