The variations of nuclear weights due to different numbers of neutrons are called isotopes. Atoms are not weighed in grams but compared to other atoms. Thus hydrogen has an atomic weight of 1.008. If all hydrogen had only a proton in the nucleus the atomic weight would be 1.000. The .008 part is due to the small population of the heavier isotopes.
Opposite charges attract.
The electrons are not pulled into the nucleus because they are moving very fast. Like charges repel. This determines much of the electronic structure of atoms with more than one electron. They are repelling each other but they are being held together by an even stronger force, called the strong force. The strong force only operates at very short distances.