Nuclear stability is a result of the number of nucleons (mixture of proton and neutron) present in an atom. There are two types of forces that are acting in between the nucleons. The first one is the attractive force or Nuclear Force that is keeping the atom stable and second one is the Electrostatic Repulsive Force acting between protons of same positive charge inside the atom.

Now as to why the number of neutrons in heavy stable nuclei is more because as we know protons are positively charged particles thereby repulsive to each other, so the heavier the nuclei is the number or proton increases as well in result increasing the repulsive forces therefore to keep the atom from falling apart, the number of neutron has to be greater than that of proton so as to have enough attractive force to overcome the repulsive forces. Therefore, for heavy nuclei to have a stable nucleus; has to have number of neutron greater than that of proton.