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This would stop any living thing from circulating fluids in its body, and sever connective tissue between limbs. I'm all for cool sci-fi stuff, but this weapon would auto kill anything with mass-dependent structure. Blood would instantly fill the feet and depart the head.

Also, where did the mass come from? What would the equal and opposite reaction to this action be? Does the object retain it's size and somehow gain density(impossible without adding constituent material) or do the spaces between its atoms shrink to miniscule size(requiring absurd amounts of energy)?

Honestly is probably one of the most absurd weapons systems in 40k. I suppose you could justify it somehow by saying that it instead creates a magnetic connection between it and the planetary body that simulates gravity by pulling the two objects together with extreme force. But intrinsically increasing an objects gravity?

Apply handwavium, I guess.

In order for grav guns to work the way it states they do, as in crushing the armour of an enemy like a tin can, it would have to cause a singular point in the armour to increase in gravity so that it can collapse into that point. The only way to do that is by giving it more constituent matter, or decreasing the space between the atoms that make up the armour (thus shrinking it to miniscule size.)

Altering the Higgs field to produce more graviton concentration in a single point is a nice thought, but I have to point out that gravitons aren't made of nothing and this is essentially the same as adding more constituent matter to the system. This has to come from somewhere. This would produce a gravitational Vacuum of sorts as everything in a certain radius would have gravitons from it pulled into the system, possibly killing the user or making his equipment useless or other various effects. However much you increased the gravity, you MUST decrease the gravity of the universe in the immediate surrounding area(actually the rest of the entire universe, as gravitons shifted places ever so slightly towards the effect you just created, but the effect would only be really noticeable close to the anomaly). The effect would proceed in a manner describing the inverse square law. (I think). This also produces the problem of having to calculate precisely how many gravitons are needed to kill each individual object without damaging the surroundings, while having no way to weigh the object in question. I really don't think this is plausible.

Furthermore, once you start this process, why does it stop? What causes it to "know" the object doesn't need any more gravitons? This isn't something you can hook up to a computer chip and just count gravitons. You will have created a black hole, or another scary gravitational anomaly, perhaps one we don't know about yet.

Honestly, shrinking the space between the atoms is something that is more plausible in terms of weaponization, as you could produce an extremely high energy containment field that forces the atoms into each other, like a nuclear fusion reactor. But at that point, you're already melting the living gak out of things within the field, and they would be turned into a plasma ball anyways... so why exert more energy to increase the mass of the object? Why not just do this inside your gun to a smaller object and fling it out the end at the enemy(plasma guns)

As far as I know, in physics, one cannot increase an objects gravity without changing what it is, or increasing it's speed relative to that of light.

Something else neat that the graviton field interpretation would also do, is increase that object's intrinsic time passage relative to it's environment. The object would, from it's perspective, watch the battle unfold in a picosecond. You wouldn't even have to kill the object to take it out of the fight. You would be aged and dead before it could react, simply sitting in this chamber of increased gravity. It's death would be inevitable, however.

Disclaimer: I am not a physicist.