On yesterday's episode of Mythbusters they tested the myth that birds in a trailer decrease the weight of the trailer when the birds take flight. The 'busters put a bunch of birds into a trailer, weighed the trailer + birds, and then allowed the birds to fly in the trailer, measuring the weight every fraction of a second. The myth was rejected because, while the weight fluctuated a fair bit, the mean weight remained the same before and after the birds took flight.
When a bird (or anything else that flies) gets airborne, it must exert a downward force equal to its weight. The weight of the trailer + birds does not change if the birds are grounded or airborne because the birds are either contributing to the weight via sitting on the trailer or by exerting a downward force by flapping their wings. The weight varies around the mean (rather than stay constant at the mean) because there is a lot of noise in the system. When the Mythbusters tried the experiment with a model helicopter, the weight stayed much more stable; but, it's important to note, the mean weight of the trailer + flying object did not change.
Why do I bring this up? I grow up flies for the purpose of isolating lots of DNA from their tissues. Before I begin a DNA extraction, I make sure to have about two grams of flies from a given line. To determine how much fly material I have, I weigh them in a vial on a scale. But the little suckers fly around in the vial, which can lead one to worry that the flying flies aren't being weighed. There's nothing to be concerned about, however, as the flies in flight are being counted each time they flap their wings.
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Seems like you've got less to worry about than the mythbusters. Your vial is a closed system (it's sealed, right?), whereas air can get in and out of the trailer. But maybe I should let a physicist handle this question...
If its really a closed system the time average weight will not change. So unless the flies have invented anti-gravity you shouldn't have to worry. On a short enough time scale the weight might fluctuate, as the center of gravity of the closed system accellerates, and turbulent eddies momentum transfer will vary over time -but this time scale is likely to be a few ms.
Your fellow ScienceBlogger Jason mentioned this question in a post a while back. Seems that Marilyn vos Savant has also tackled this in one of her columns.