Is gravity really a force that occurs between composite "objects," or is it individual atoms? The standard explanation of gravity (according to Google's dictionary) puzzles me:

Gravity is the force that attracts a body toward the center of the earth, or toward any other physical body having mass.

The whole idea of a "body" or an "object" is really just a human invention. It's a communication tool that allows us to refer to a mass of atoms. When we say "earth" we mean all the atoms in the atmosphere, on the surface, and inside the core of the planet. But from the point of view of pure physics, there is no "earth," just a collection atoms, right? Similarly, there is no "me", just a collection of atoms that are held together through chemical bonds and a semi-permeable membrane (skin).
At first I was thinking "maybe by 'body' it means a collection of atoms that are chemically bonded to each other into molecules, crystals, etc?" but then I realized the earth's gravitational field is made up of many things that aren't bonded. Like, all the water in the ocean isn't bonded to the molten iron in the earth's core, but the mass of both of them counts towards the earth's total mass, and adds to the gravitational force that earth exerts on nearby objects, like the moon.
So my question is, how does gravity really work? If it's not at the level of composite "bodies", it seems like it must be at the level of the individual atom. Here's how I'm guessing it works, but I would love to be corrected if I am wrong:
Each atom in my body is individually affected by the force of all other atoms nearby (proportional to the mass and the distance of the atom). Because there are way more atoms beneath my feet than above my head, the net effect on each atom in my body is to be pulled down towards earth. So an atom at the top of my head has slightly less gravitational force acting on it than an atom at the bottom of my shoe, because it's a tiny bit further from the most of the atoms in the earth. And the atom at the bottom of my shoe is being pulled up slightly by the atom at the top of my head, but the net effect is for it to be pulled down, because there are more atoms beneath it.
But it's not like there is a thing called "earth" that has a certain mass and thus exerts one singular gravitational force on nearby bodies like "me", right?
Is this right, or am I missing something? I am very interested in learning more about this!
 A: We usually speak of gravity in macroscopic terms (body, object, etc) but you are correct that gravity is also felt by microscopic entities (atoms, elementary particles, etc). Gravity is a much weaker force than the forces that bind atoms, molecules, nuclei, etc so it makes more sense to use the macroscopic language when considering gravity. There is also the fact that gravity affects massless entities (photons, etc) as well, and that the masses of composite objects are not exactly the sum of the masses of their constituents (binding forces can add or subtract from an object's mass, depending on the circumstance). 
A: Gravity interconnects all mass and energy that exists in the universe. The attractive force between particles drops off exponentially, so after a certain distance it's essentially neglible. To answer your question, particles do not need to be part of an atom to attract and be attracted to other masses. As to how gravity works, that is one of the great unsolved mysteries of modern physics. Curved spacetime helps us cope with what we experience, but it doesn't provide insight into the true nature of gravity (assuming there is more to learn).
A: Atoms are not what their name implies from its etymology, indivisible particles, instead they are highly complex objects where all four forces of nature interact, gravity being the weakest one, by far. So while you are right that "body" and "Earth" are human inventions, well so is "atom".
Gravity is a universal interaction arising from the fact that a concentration of energy deforms the spacetime continuum. Since all inertial objects basically move by following the most direct way in spacetime, this deformation affects their trajectory and it appears to us that masses attract masses, because masses are the most concentrated forms of energy. Note that by "object" I here mean any physical system, not only macroscopic ones. 
At the scale of our planet and its inhabitants, it is a very good approximation to say that "Gravity is the force that attracts a body toward the center of the earth". The key here is that Earth being very close to a central-symmetric distribution of mass, the gravity felt outside it is mathematically the same as the gravity that would be exerted by its whole mass being concentrated in a single point at its center (mathematically only, because physically concentring too much matter in a too small area results in a black hole).
