Is gravity weaker when there is a mass obstructing? If gravity were an exchange of particles it seems reasonable to me to assume that a mass between two other masses would lessen the attraction between the two outer masses, as the exchange particles would be absorbed. This is not considered at all, so I assume I am wrong, why?
 A: 
If gravity were an exchange of particles it seems reasonable to me to assume that a mass between two other masses would lessen the attraction between the two outer masses, as the exchange particles would be absorbed.

Let us clear up the model you have in your head.
Exchange of particles means a quantum mechanical model for gravity, i.e. quantization of gravity. This is something that has been used in cosmology, the inflation period, as an effective quantization.
Exchange of particles is a model used withFeynman diagrams, where the exchanged particles are virtual.

In this electron electron scattering, the photon exchanged is virtual, i.e. it has the quantum numbers of name "photon" but its mass is off mass shell, because it is under an overall integral and varies with the energy and momentum conservation under the integral limits.
A simple  hypothetical gravitational model would have two masses incoming, two masses outgoing with real four vectors,  exchanging a graviton to scatter/interact  with each other gravitationally.
In such a model, the macroscopic gravitational field will be built up  by virtual graviton exchanges similar to the way a macroscopic electric field attraction is built up by virtual photon exchanges when looked quantum mechanically.
If you have three masses, it becomes a complicated problem, but it is evident that the masses will be exchanging gravitons, each mass attracting the other two. As gravity is a very weak interaction, probabilities of interaction are low and there will be virtual gravitons going through each mass without interacting .
It is simpler to go to the classical gravitational fields to see that there is no shielding. Each of the three masses interacts gravitationally with the center of mass it sees of the other two, and thus there is no shielding, because the masses are additive classically, and there is a larger gravitational field because of the addition.
Gravity has not yet been definitively quantized , but in physics a mainstay is mathematical continuity between frameworks, classical and quantum mechanical. The classical has to emerge smoothly from the quantum mechanical. The above discussion assumes that this will be the case when a definitive model with quantized gravity is proposed, ( probably a string theory model which already has quantization of gravity, but has not been defined yet) 
A: Hypothetical gravitons have no mass and do not interact with the other forces of nature. Gravitons would pass through massive objects at the speed of light without interacting with it.
A: Some force carriers do have rest mass, some do not. The force carriers of EM, photons do not have rest mass, gluons, for strong force too. 
W and Z bozons for the weak interaction do have rest masses.
If gravitons do have masses, there is an upper limit on their mass, based on the analysis of gravitational waves, their compton wavelength is at least 1.6 lightyears, so their mass is no more then 7.7*10^-23eV/c^2.
The reason for some force carriers to have mass (or bigger mass) is the length of the interaction. EM and gravitational forces are long range forces.
You can see that EM interactions can have infinite length, that is why photons do not have rest mass.
So does the graviton have no or very small mass, so the force can be long range.
For the weak interaction, since it is short range, W and Z bozons have masses 100 times the proton.
The strong force is mediated by the gluons, they do not have rest mass, but it is still a short range force. It is because gluons interact with each other, and they stick together and form strings. the force between them does not weaken with distance it is constant.
Your question says that the exchange of gravitons would lessen the mass because gravitons would be absorbed. We do not know if gravitons are absorbed or not. What you are suggesting is that like with the nuclear force, there is a mass defect. There might be, what we need to check is if two masses that are interacting gravitationally, would be less heavier together then measured separately. I do not know if anyone has made an experiment like that.
