No. There's been a lot of arguing about terminology regarding "mass" and "weight". From what I remember in undergrad physics - the mass of any element is the number of protons in its nucleus: hydrogen has a mass of 1 - (1 proton); helium's mass is 2 (2 protons)...etc. Mass defines the element - if you changed the number of protons - you change the name of the element - with all of its characteristics changed as well. Weight is directly related to the effect of gravitational force on an element with mass - (if you have a piece of lead on earth, weigh it, take it to the moon, it will weigh less - but it's still lead and the term "weight" really means "gravitational force"on a mass in a particular environment). Now comes the controversy - here's the basic definition of atomic weight: An atomic weight (relative atomic mass) of an element from a specified source is the ratio of the average mass per atom of the element to 1/12 of the mass of an atom of 12C (Carbon 12). - Wikipedia
These two aren't the same as many people wrongly think. Atomic mass is the mass of a specific isotope; it's the total mass of the protons, neutrons and electrons in a single atom. Atomic weight, on the other hand, refers to the ratio of the average mass of the atoms of an element to 1/12 of the mass of a carbon-12 atom. See en.wikipedia.org/wiki/Atomic_mass and en.wikipedia.org/wiki/Atomic_weight for more on this.