The reason that the sum of proton numbers in an element's atoms never exceeds their atomic weight is due to the presence of neutrons in the atomic nucleus.
Protons are positively charged particles found in the nucleus of an atom, and they determine the atomic number of an element, which defines its identity. The atomic number represents the number of protons in the nucleus.
Neutrons, on the other hand, are particles with no electrical charge that also reside in the nucleus. They contribute to the mass of the atom but do not affect the atomic number.
The atomic weight of an element takes into account both protons and neutrons in the nucleus. It represents the weighted average mass of all the isotopes of that element, considering their abundance. Since neutrons contribute to the atomic weight without affecting the atomic number, the sum of proton numbers in an element's atoms does not exceed the atomic weight.
In summary, the presence of neutrons in the nucleus allows for variations in the mass of atoms of the same element (isotopes), while the atomic number (determined by the number of protons) remains constant. The atomic weight accounts for these isotopic variations and is the weighted average of the masses of the different isotopes.