Atomic mass (ma) is the mass of an atom. A single atom has a set number of protons and neutrons, so the mass is unequivocal (won't change) and is the sum of the number of protons and neutrons in the atom. Electrons contribute so little mass that they aren't counted.
Atomic weight is a weighted average of the mass of all the atoms of an element, based on the abundance of isotopes. The atomic weight can change because it depends on our understanding of how much of each isotope of an element exists