Well it certainly does for wood or anything else that floats. It essentially weighs less than zero in water.. i.e. has positive buoyancy.. The same principle so discovered by Archimedes to elucidate the purity of metals, is not often thought of by the average man. Archimedes was looking for a non destructive way of determining the purity of the King's Golden Crown, and exactly how much of what metal was in it that changed it's purity. One day when he sank into his bath, he noted the pressure of water that he displaced could be measured by the level of the bath water in the tub and thus his weight relative to water. His agile mind probably further noted that the lighter wooden ducky he played with displaced a fair amount of water, but the silver ducky displaced less. You can then understand why Archimedes ran naked thru the streets yelling, "I have found it". Anybody might do this after playing with duckies and making such a breakthrough. Archie was able to determine that the impurity of the crown was copper and exactly 10% or something like that, by making a chart of what gold and copper would be for any two percentages. All of them unique. Gold and copper were the subject of a lot of literature about purification of such, as much gold came from copper metal in Egypt and Spain.
A complication occurs if you have three metals, gold, copper and silver. Do you think it is possible by means of SG in air and water to determine the exact weight of each in a mixture? Is there a unique SG for each value? For two metals only there is only one SG or combined weight for every differing percentage and this may be shown as unique for every two metals if you know or hold one metal as known of type. There are no two combinations of X per cent copper and 100-X per cent gold that have the same SG.
The problem is it would be possible for a mixture of two metals, say of copper and gold to equal a mixture of silver copper and gold in SG. 67.466% gold and 32.533% silver is equal to 71% gold, 9% silver and 20 percent copper. These mixtures both have the same volume for their weight, so weigh the same in water. Is there a way for Archimedes to have resolved this without testing the crown's metal by assay? Archimedes would know that at over 20% gold the crown would appear silver in colour. But this is not definitive as to exact weight of silver, copper and gold.
Archimedes was able to do this:
... when Archimedes began to ply his engines, he at once shot against the land forces all sorts of missile weapons, and immense masses of stone that came down with incredible noise and violence; against which no man could stand; for they knocked down those upon whom they fell in heaps, breaking all their ranks and files. In the meantime huge poles thrust out from the walls over the ships and sunk some by great weights which they let down from on high upon them; others they lifted up into the air by an iron hand or beak like a crane's beak and, when they had drawn them up by the prow, and set them on end upon the poop, they plunged them to the bottom of the sea; or else the ships, drawn by engines within, and whirled about, were dashed against steep rocks that stood jutting out under the walls, with great destruction of the soldiers that were aboard them. A ship was frequently lifted up to a great height in the air (a dreadful thing to behold), and was rolled to and fro, and kept swinging, until the mariners were all thrown out, when at length it was dashed against the rocks, or let fall.
So it is clear that he was a man of no ordinary mind. Ships back then held several hundred men, so they were not toys, perhaps weighing as much as several hundred tons. To design a machine that will lift them easily is not trivial.
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