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 (mass spectrometry)
The nominal mass for an element is the mass number of its most abundant naturally occurring stable isotope, and for an ion or molecule, the nominal mass is the sum of the nominal masses of the constituent atoms. Isotope abundances are tabulated by IUPAC: for example carbon has two stable isotopes C at 98.9% natural abundance and C at 1.1% natural abundance, thus the nominal mass of carbon is 12. The nominal mass is not always the lowest mass number, for example iron has isotopes Fe, Fe, Fe, and Fe with abundances 6%, 92%, 10%, and 2%, respectively, and a nominal mass of 56. For a molecule, the nominal mass is obtained by summing the nominal masses of the constituent elements, for example water has two hydrogen atoms with nominal mass 1 and one oxygen atom with nominal mass 16, therefore the nominal mass of HO is 18.