Objects don't become heavier under post higgs standard model as they approach the speed of light they just become heavier because as you add energy it interacts more with the higgs field. The mass of an object moving at the speed of light is still the same it was when the object was at rest it's just harder to accelerate.
I think I see what you are saying there. It will take a while for me to get my mind around Higgs science so don't worry too much. After all I have been working on learning the current styles for a long time now.
The Higgs field is nothing special it is a normal field you see the same behaviour in an electric and magnetic fields you would know them as lenz's law and faradays law or back emf.
As those laws show that movement in a field is normally resisted or opposed that conservation of energy thing.
So the higgs field is simply another sort of field that reacts with quantum spins thus some particles see the field others do not giving the mass properties to the differenet particles and movement is opposed.
Is this due to a change in the gravitational mass or is it the gravitation of the energy supplied to the object that causes an increase in gravity?
The gravity issue has not been resolved with the Higgs mechanism and standard model it is not a theory of everything it does not answer the questions on gravity.
The problem lies in the fact gravity is so weak and since the Higgs boson effect could mix with the scalar graviton, since there is no reason to forbid a coupling of the Higgs field to the gravitational scalar curvature it may or may not play a role in gravity.
Theoretically gravity could be yet another field with a much weaker interaction it is sort of envisaged that way in the standard model or it could be a more exotic effect. In the standard model gravity is carried by a theoretical particle the graviton and it would interact either thru a new field or with the existing fields.
We are less than 6 months into a new era when we have added in another force and there will be many many tests on the Higgs field to try and isolate it and probably at that point we will be in a much better position to speculate on gravity.
The Higgs field and it's mass effects had wrongly been classed as gravity and this has hindered the understanding of gravity. I suspect the next couple of years will narrow gravity possibilities down and ultimately lead to conclusive tests similar to how science hunted down the Higgs.
