If you had a perfect scale, the reading would fluctuate based on
$$\delta w = m\ddot{x}_{cm}$$
$\delta w$ is the size of the fluctuation in the reading, $m$ the total mass on the scale (including fly and air), and $\ddot{x}_{cm}$ the acceleration of the center of mass.
Integrating over time,
$$\int_{time} \delta w(t) = m\Delta(\dot{x}_{cm})$$
Here, $\Delta(\dot{x}_{cm})$ is the change in velocity of the center of mass over the period you observe the readings. Because the velocity of the center of mass cannot change very much, if you integrate the fluctuations over time, you wind find that their average tends towards zero. If the fly begins and ends in the same place and the air is still, the fluctuations integrate out to exactly zero.
Whenever the fly is accelerating up, we expect the reading to be a little higher than normal. When the fly accelerates down, we expect the reading to be a little lower than normal. If the fly hovers in a steady state, the reading will be the same as if the fly were still sitting on the bottom.
A real scale cannot adjust itself perfectly and instantaneously, so we would need to know more details of the scale to say more about the real reading.
Freeze it in liquid helium. Any gas inside will condense out.
Spin it quickly then stop it. The internal turbulence of the spinning gas will be visible with a sensitive detector.
Apply a short sharp impact to one side. If there is gas inside, the sound energy peak from the sound transiting the gas will be temporally distinct from the spectrum of the sound transiting through the glass.
Best Answer
You send the box and liquid towards a barrier equipped with a gauge to measure force. The setup looks like:
When the box hits the barrier it stops, but the liquid inside it keeps moving. A short time later the liquid hits the side of the box and it too stops moving. So when you record the force at the barrier as a function of time you will get two peaks, first as the box hits the barrier and stops, then a short time later a second peak as the water hits the end of the box and stops.
If you integrate the force time curve you will get the impulse during the collision, and this is equal to the change of momentum. Since momentum is $mv$, and you know the velocity $v$, you can calculate the mass. The two peaks will give you the mass of the box and the mass of the liquid.
Needless to say, in real life you will get only approximate results. The peak for the box should be clear, however the viscosity of the liquid will mean there is a force exerted on the barrier while the liquid is moving and before it hits the end of the box. Also the liquid will splash, so the impulse you measure will be too high. However the method should give you an approximate result.