ORIGINAL: Lomcevak Duck
After thought: In the fish tank example-
The balloon, boat, and bird are all creating their own "lift or buoyancy" when they are working properly. Take the wings away from the 2oz. bird, and he falls to the floor and adds to the overall weight. Cut the boat and the boat sinks and adds to the weight. Poke a hole in the balloon and it falls to the bottom of the fish tank and adds to the overall weight.
Sorry, no. In all cases, the bottle/tank/etc is capped....closed. So you have closed systems.
The bird's mass is part of the total mass of the container and its contents. Whether it flies or not, that mass is always there. Its flight is just moving the air around that's already inside the container. If the bird quit flying and fell to the bottom, only an acceleration would be noted as the bird hit the bottom.
With a balloon, the envelope, payload, and filling gas all have mass, which is part of the mass of the entire container. You can deflate the balloon and move the items around, but the mass remains the same.
Same with the boat in the sealed tank example. Whether it floats or not, the mass of the system doesn't change.
Weight is nothing more than mass x acceleration of gravity. If mass doesn't change, neither does weight.
You can't make an airplane lighter by having the birds (bees, whatever) fly inside it. Their mass is always part of the total mass of the airplane and cargo until you let them out.