How does existence of graviton helps explain 2 different objects fall at the same rate? Actually I want to see how gravitons help to explain why a feather and a bowling ball would fall at the same rate towards the ground assuming no air resistance, I would imagine bowling ball to emit more gravitons than a feather since it is much more massive but how about the attractive force of earth working on both feather and bowling ball?
 A: A graviton is a hypothetical elementary particle used in the effective quantized gravity in cosmological models.

Actually I want to see how gravitons help to explain why a feather and a bowling ball would fall at the same rate towards the ground assuming no air resistance,

This was an observation that led to Newtonian gravity, and Newtonian mechanics is valid in the macroscopic dimensions, whether gravity is quantized or  not (i.e. established existence of gravitons). The quantum gravitational theory should be able to show mathematically how the classical theory emerges from it, similar to how classical electromagnetic theory is emergent from the underlying quantum electrodynamics. It is not simple, and it needs knowledge of quantum field theory.
A: The existence of gravitons or non-existence of gravitons has nothing to do with the observation that all bodies fall all at the same rate.
Consider electromagnetism: the discovery of photons did not provide a new view on Coulomb's law.
So gravitons will not provide a new picture on the rate massive bodies fall on each other.
Actually, the observation that all massive bodies fall at the same rate is an expression of curved space-time. If bodies should follow geodesics in curved space when not exposed to other non-gravitational forces. I.e. they should fall at the same rate independent of the mass.
Therefore the question why all bodies independent of their mass fall at the same rate is already solved ... no further "help" is needed.
Imagine, initial and gravity mass would not be equal, so bodies would fall at different rate depending on their mass. So we would have a different gravity theory. Such a theory could also be quantized, and as a consequence would have quantized modes, i.e. gravitons. So the existence of gravitons does not tell us about the true theory of gravity. (Possibly the gravitons in one or the other theory might have different properties, but this is not the question here).
Moreover, gravitational radiation is actually quadrupolar: Therefore on could wonder if any (non-virtual) gravitons --- if they existed --- would be emitted during the fall. Only if the system falling body + earth (or any other huge massive object) have a quadrupolar moment, they would emit gravitational radiation which could manifest as gravitons if they were exposed to experiments that could reveal their quantum properties.
In particular the initial conditions of the free fall can be chosen that no quadrupolar moment is created whereas the free fall still is independent of the mass of the falling bodies. So in this case no (non-virtual) gravitational waves are generated.
A: "How do gravitons help to explain ..."
Gravitons are not introduced in order to explain classical features of gravity, such as the fact that objects of different mass have the same acceleration under gravity. Rather, one takes an interest in finding out whether there can be some sort of quantum theory of gravity (for which general relativity provides a classical approximation). In a quantum theory the basic idea could, for example, be a quantum field. In that case excitations of the field can be studied, and they are called gravitons.
So now the question is no longer "how do gravitons help to explain the universality of free-fall"; it becomes "how does the universality of free-fall come about in a quantum theory of gravity". The answer to that is that this universality is built into the structure of the theory from the outset. For example, one could build it in by making sure there is the appropriate relationship between inertial mass and gravitational mass (i.e. they are the same). Inertial mass is treated in field theory in a two-step approach. First one just asserts that each kind of field has excitations that have some given inertial mass (e.g. the excitations of the electron field have the mass of the electron, the excitations of this or that quark field have the mass of the relevant quark, etc., and the excitations of the gravity field have zero rest mass). Then, in a more complete analysis, one connects the inertial mass to interactions with the Higgs field. So you see now it is becoming quite complicated, and there is no quick answer to your question. The best answer is probably to say that in proposing a quantum theory of gravity (something no one has yet done in full) one would be well advised to keep the theoretical structure in touch with the geometric ideas of classical general relativity, because then the feature asked about (the universality of free-fall) will be part of what the theory predicts.
A: Graviton does not exist, it is just a model. All physics models are just mathematical models. We just use mathematics to predict what will be happened.
