The weight, or mass, of a nucleus is significantly greater than the mass of an atom as a whole. This is because the vast majority of an atom's mass is concentrated within its nucleus.
The nucleus of an atom contains protons and neutrons, which have approximately equal masses. The mass of a proton is about 1 atomic mass unit (u), and the mass of a neutron is also approximately 1 atomic mass unit. In comparison, the mass of an electron is extremely small, roughly 1/1836th of the mass of a proton or neutron.
The total mass of an atom is determined by the sum of the masses of its protons, neutrons, and electrons. However, due to the relatively tiny mass of electrons compared to protons and neutrons, the mass of electrons is usually considered negligible when calculating the total atomic mass.
As a result, the weight of a nucleus is roughly equal to the sum of the masses of its protons and neutrons, while the weight of an atom is slightly higher due to the inclusion of electrons. Therefore, the nucleus accounts for the vast majority of an atom's weight.