You're right on the money about gravity, Homer - there's a constant, G, which is the gravitational constant. One of the many gifts that dapper chap Newton bestowed upon the scientific world. It is indeed true that the effect of gravity lessons as distance between two bodies increases, while the gravitational constant remains the same. More accurately, it lessens as the distance between two object's center of mass increases. We would get heavier as we approached the Earth's center.
They have equations for this and everything. Very slick. You could find out the gravitational force between yourself and a lady you happen to fancy. Just work out the figures, hand her a slip of paper and she'll have no choice but to succumb to the scientific evidence.
But I dunno about this "
ripping atoms apart" aspect of the theory. It's actually not gravity that holds atoms together... gravity is the weakest of the Four Fundamental Forces (F3 - dramatic, imposing, yet elegant

). It's the strong (and weak, I think) nuclear forces that bind atoms together. These forces are so powerful that they supply the energy that can result in nuclear explosions. They are ridiculously more powerful than gravity - there's a lot of decimal places involved, I remember that much.
I don't know enough to say that it's *impossible* for this supposed anti-gravity to one day (in the absurdly distant future) overcome these forces, but it seems highly doubtful.