Weight and mass are not synonymous.
Weight is a force.
The weight of an object depends on its location - things can weigh differently in different places.
The first thing to realize about weight is that weight is not the same as mass, even though the terms are used synonymously in everyday life. Mass measures inertia - it is a property of an object. Weight is a force - something that happens to an object.
Physicists and engineers all agree that weight is a force, but there is considerable disagreement and confusion about what force weight is - different textbooks say different things, and some textbooks say different things in different places. Mostly, opinion is divided into two camps. For some people, "weight is the force of gravity", and for others "weight is what a scale reads". You might think that the two statements are equivalent - but they aren't. There are advantages and (unfortunately) disadvantages with either point of view.
Our text, among others, says:
Weight: The force of gravity upon a body.1
This is not the intuitive, laymen's definition of weight. You can't feel the force of gravity. You feel the floor pushing up on you, not the downward pull of the Earth. You don't feel pulled toward the Earth, even when you jump into the air.
There is a standard definition of weight, given by the International Organization for Standardization (ISO) which says:
The weight of a body in a specified reference system is that force which, when applied to the body, would give it an acceleration equal to the local acceleration of free fall in that reference system. - ISO 31-3 "Quantities and Units. Part 3, Mechanics", 19922
Can this be simplified without losing precision? Yes! It turns out that this definition of weight is equivalent to saying:
Weight is what a scale reads.3
which is equivalent to saying:
An object's weight equals the force required to support it.4
It seems at first that this is a much more natural, practical and useful way to look at weight than associating weight directly with the force of gravity. ("What a scale reads" and "the force of gravity" are not always equivalent - see The Elevator Problem for details...) This definition - weight is what a scale reads - also fits quite naturally with the idea of "weightlessness".
In order to use this definition effectively in applications requires a pretty sophisticated understanding of Newton's Laws - particularly Newton's Third Law - which most beginning physics students generally don't have. (No offense intended...)
In this course, we will follow the text's lead, and say that an object's weight equals its mass times g.
1 Hewitt, Conceptual Physics, p32
2 Weight - An Official Definition, Mario Iona, The Physics Teacher, Vol 37, p. 238 (April 1999)
3 adapted from Weight - An Accurate, Up-to-Date, Layman's Definition, Roy Bishop, The Physics Teacher, Vol. 37, p. 238-239 (April 1999)
Weight and Gravity - The Need for Consistent Definitions, Richard C. Morrison, The Physics Teacher, Vol 37, p. 51-52 (January 1999)
Weight - A Pictorial View, Andrzej Sokolowski, The Physics Teacher, Vol 37, p. 340 (April 1999)
Weight - Don't Use the Word at All, Ronald Brown, The Physics Teacher, Vol. 37, p. 341 (April 1999)