ORIGINAL: Tall Paul
...If the aquarium is filled to the top with water, and the submarine is then placed in it, the excess water slops over.. Eureka!

The weight on the scale changes, relative to the mass of the sub relative to the mass of the displaced water.
Actually if the submarine is set to neutral bouancy and you do this the weight on the scale of the full tank before and after the sub is added won't change. You see, if the sub is nuetrally bouyant that means it has the exact same density as the water it displaced over the edge. So the weight of the water over the edge is the same weight at the sub so the scale does not change. Niether will it if the sub is floating on top since it's weight still is reflected by the water pushed over the side. Only if it's heavy enough to sink to the bottom will the scale register a gain in weight. The amount being equal to the difference between the "heavy" sub and the water pushed over the side.
The same will apply to the hydrogen balloon put into the big plastic pail of air. The overall density of the weight and the balloon matches the air it displaces. It has to or it would not float evenly. Put this combo into a bucket with a lid on it and it'll register the same mass as if it was filled with only air since the air you replaced by adding the balloon is the same density as the balloon and weight. And because of this if you suddenly accelerate the bucket the balloon and weight will swing about due to the apparent shift in gravity direction but unless part of it hits the side of the bucket the balloon and bob will tend to try to stay in the same spot within the bucket..... Just like if you slop a jelly fish around in a bucket of water and the water comes to rest the jelly fish is still more or less in the same spot.