The term "atomic weight" can indeed be a bit misleading, as it does have historical roots in the concept of weight. However, in the context of atomic weight, the term refers to the average relative mass of an atom compared to a standard reference.
Atomic weight is determined based on the relative abundances of different isotopes of an element and their respective masses. Isotopes are variants of an element that have the same number of protons but different numbers of neutrons. These isotopes occur in different proportions in nature.
To calculate the atomic weight of an element, scientists take into account the masses of each isotope and their relative abundances. The atomic weight is a weighted average of these isotopic masses, where the abundance of each isotope serves as the weight.
The atomic weight scale is based on the carbon-12 isotope, which is defined to have an atomic mass of exactly 12 atomic mass units (u). Atomic mass units are not units of weight in the conventional sense, but rather a unit of mass used specifically in the context of atomic and molecular masses.
It's important to note that atomic weight is not influenced by gravity. The determination of atomic weights does not rely on gravity and can be determined in free space or in any environment. It is a property that remains constant regardless of the presence or absence of gravitational fields.