It depends on the context.
In commerce and law, the terms mass and weight are synonymous. That means that when you see a can of beans in an American grocery store and it is labeled as “NET WEIGHT 1 lb (453 g)” it is totally correct from a legal and commercial point of view: “WEIGHT” means what physicists call mass, the pound (lb) is legally a unit of mass and not of force (contrary to the opinion of many misinformed engineers and scientists), and the gram (g) is defined to be a unit of mass, so everything is self-consistent. (For those who doubt this, traders used pan balances and reference weights for many centuries before Newton and Hooke clarified the interrelationship of mass and gravitational force and the spring scale was developed. The terms “weigh” as a verb for the process and “weight” as a noun for the measurement as well as for the reference objects used to counterbalance the unknown quantity have been conventional nomenclature for many centuries, and we still hear about weights and measures agencies for which “weights” refers to standardized masses. The pound is defined in the UK by law and in the US by the National institute of Standards and Technology as 1 lb = 0.453 592 37 kg, which because of its equality with a mass value means the pound must be a mass; there is authorization to have a force unit, but the suffix “-force” must be appended to “pound” and “f” appended to the symbol “lb” to indicate that the force unit rather than the standard, default pound is intended.)
In physics, the term mass is used to mean the amount of matter, which is associated with inertia, whereas physicists insist on restricting the word weight to refer to the force of gravitational attraction on a mass, which is the product of the mass of an object times the strength of acceleration of gravity where the object is. Physicists tend to insist that the frequent use of weight in the sense of mass by the general public, traders, and lawyers is totally erroneous; however, they are the ones who in the early 1700s took the well-established word weight with its well-established meaning of what physicists now call mass and tried to force a very unnatural change to the meaning. The physicists are the ones guilty of corrupting a conventional word and traditional meaning and then hypocrtically blaming the general public for misusing the term.
In chemistry, weight is commonly used to refer to the average mass over all atomic isotopes or molecules of a substance as the atomic weight or molecular weight, respecively of the substance; for individual isotopes the mass is commonly referred to as relative atomic mass, so there is some inconsistency. Such masses/weights are measure in unified atomic mass units (u) or daltons (Da), not in kilograms/grams nor in newtons, so using grams to discern mass and newtons to discern weight force has no applicability here.
