The Atomic Mass of an element is specific to each isotope. So Deuterium has a different atomic mass than Tritium. The Atomic Weight of an element is a calculate value based upon the % Isotopic Composition of the element. The atomic mass/weight is given in terms of Atomic Mass Units which = 1/12 the mass of a Carbon 12 atom. A Carbon 12 atom has 6 neutrons and 6 protons, so scientists said that an proton/neutron is equal to 1/12th the mass of a Carbon 12 atom and defined this mass as an Atomic Mass Unit. (The exact calculations are pretty neat, and are usually explained in a general chemistry textbook). The weights you see on a periodic table, are the averages of the Atomic Masses of the element's isotope based upon the isotopic abundance. To calculate this, a purified sample of the element, in what is considered its 'natural isotopic proportion', is run through a Mass Spectrometer. They are then able to see what percentage of that element is composed of each isotope. So for example, let's say Element X has two isotopes. They are X-95 and X-99. They then run this pure element through a mass spec and see that 72% of it is X-95, and 28% is X-99. To calculate the Atomic Weight seen on the periodic table, they use the formula (0.72*95)+(0.28*99) = 96.12 which is the atomic weight they would report. The accuracy of the atomic weight reported is what can constantly change. You have to run a LARGE number of samples and have a Mass Spec which is very accurate in order to get the large number of significant figures. This is why weights can change over time, however by now they are mostly set in stone up to a certain number of decimal places. However, as techniques are derived to get more accurate results on the Isotopic% for each element, the reported weights can get even more accurate. Did that make sense?