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.
Mass in general relativity
In special relativity, the invariant mass or "rest mass" ("hereafter simply "mass"") of an isolated system can be defined in terms of the energy and momentum of the system by the relativistic energy–momentum equation: