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.
Molecular mass
Both atomic and molecular masses are usually obtained relative to the mass of the isotope C (carbon 12), which by definition is equal to 12. For example, the molecular mass of methane, whose molecular formula is CH, is calculated as follows:
A more proper term would be "relative molecular mass". However the adjective 'relative' is omitted as it is universally assumed that atomic and molecular masses are relative to the mass of C. Relative atomic and molecular mass values are dimensionless but are given the "unit" Dalton (formerly atomic mass unit) to indicate that the number is equal to the mass of one molecule divided by of the mass of one atom of C. The mass of 1 mol of substance is designated as molar mass. By definition, it has the unit gram.