Well, as I do not have a degree in subatomic particles, I will pull some stuff out of my butt to cover myself while I come up with a proper response (woah, right now I feel like an FE)
All atoms emit subatomic particles with masses so low that they effect the mass of the atom very little. These particles then "dance" and transfer momentum and energy between the atoms.
WHew, that took some effort.
If a subatomic particle is responsible for gravity, I can show you my major problem with that. Lets say the world is round and all celestial bodies orbit each other due to a force called gravity. Well the earth and sun send gravitons back and forth that will cause a certain amount of attraction towards one another dependant on the quantity of gravitons and in what direction they came from or what message they might contain.
Heres my problem: There is a potential energy in the sun and earth due to their distance. Meaning that they have the energy to fall to each other and collide with massive energy. Now if a graviton exists, what if something interferes with its path or message? What if the sun is told to be attracted to the earth in a different direction? That would violate the whole principals of newtonian physics. It would mean you could create energy from nothing.
This is due to the fact that the idea of gravitons implies that the sun has the ability to accelerate itself in any direction. All it is doing is waiting to find out what vector of acceleration to apply. This is inconsistant with many theories. The force of attraction on the sun, must be a direct cause of the earth and visa versa.
Additionally, gravity is a pulling force. In physics, a very basic lesson is there is no such thing as a pulling force, only a pushing one. These can be complicated, so as to seem like a pulling force when it is actually a series of pushing ones. This makes me inclined to believe in gravity (and magnetic and electric) forces that are a series of pushing ones. But that is off topic. If you want to know more I will explain elsewhere.