Good Answer by Fishtoaster.
The science is ancient, discovered by Archimedes.
1: Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.
In other words, if you put a ball, with volume 1 litre completely under water, there is an upwards force on the ball (buoyancy or flotation) equal to the weight of 1 litre of water. (i.e. 1 kilogram-force or 9.81 Newtons)
2: (Corollary) Any floating object displaces its own weight of fluid.
If we place a floating object of mass 1 kilo, it will displace exactly 1 kilo of water, or 1 litre of water. If the volume of our object is greater than 1 litre (i.e. the object is less dense than water), it will float.
So, with a Hydrometer, it is weighted such that the weight of the submerged volume at the 1.000 reading is exactly equal to the weight of the hydrometer. If we dissolve solids into the water (sugar) that volume of water is heavier, and less of it needs to be displaced in order for the hydrometer's weight to be matched, and the Hydrometer floats higher.