Weight
In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a "force" that results from the action of gravity on matter: it measures how strongly the force of gravity pulls on that matter. However, in most practical everyday situations the word "weight" is used when, strictly, "mass" is meant. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass.
Kilogram
Because at any given point on Earth the weight of an object is proportional to its mass, the mass of an object in kilograms is usually measured by comparing its weight to the weight of a standard mass, whose mass is known in kilograms, using a device called a weighing scale. The ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses.