Guys here's my simple explanation:

If the bird were dead - then it would result in a dead weight.
But, since the bird is alive flying inside the container, it causes turmoil in the air due to its momentum and inertia producing vector forces bouncing downwards/upwards with enough magnitude to give some noticeable fluctuations on the scale display readings.

Conclusion: the measured weight is not constant, but varies with a frequency equal to the number of wing beats per second.

Prove me wrong if you bother…
[8D]