The question is on title; What if Gravitational Constant, $G$, is not constant?
Let's skip all the local consequences if it would suddenly change, like asked here; Can gravitational constant be changed? Let's also skip all the thought about if this could be proved, like asked here; What is the proof that the universal constants ($G$, $\hbar$, $\ldots$) are really constant in time and space? Also let's skip the theoretical discussions like; Can the gravitational constant $G$ be calculated theoretically? and also the discussion about if it's constant or not, like Is the gravitational constant $G$ a fundamental universal constant?
The stuff I am thinking here has nothing to do in our Solar system, as it seems that G is here as constant as the g is on Earth. And exactly as g varies between planets, it might be possible that G varies between Solar systems. Actually a variation in G has allready been noticed; and funnily enough it follows the LOD variations with a period of 5.9 Years.
But what if it's truly not constant, but varies, in different part of universe?
- Could it explain Dark matter?
- Could it explain Dark energy?
This is more complicated than Dark Matter, as evidence for Dark Energy is used Gravitational Lensing, which calculations includes G. Also the cosmic microwave background's critical density is calculated through G. The Large scale structure to again based on the same critical density. The Sachs-Wolfe effect would simply be more logical through QED explained gravity. The Hubble constant is also derived through G. The only evidence I can't close out is Supernoavae. but it seems to be Circular reasoning.
These are my main detailled problems. And I wan't to point out, that the antimatter is not to be confused in these Dark ones. Positron's are real, observed, stuff. The Dark-stuff is only hypotethical things to explain the observed problems, when G is assumed to be constant. According to Occam's razor; Among competing hypotheses, the one with the fewest assumptions should be selected. And if we assume that G is not constant, we remove quite a lot of assumptions.
The first given answer provides thoughts how the gravity could be influenced locally. I don't see this possible and I want to lead the thoughts to correct direction, So I feel it necessary to open my thoughts more. The source is this Feynman Lection. I calculated and found out, that the energy of these particles hitting the "mass only" is not enough to cause Gravity. But if we think the Solar system, it's 110- 122 AU up to the Edge of Heliosphere. (Maybe it's 137.036) Anyhow, the Voyager has detected a 100-fold increase in the intensity of high-energy electrons from elsewhere in the galaxy diffusing into our solar system from outside, this means that these electrons are colliding the few atoms at 120 AU away from the sun; and thus these atoms will have a velocity. And as they will hit more an more atoms, the pressure grows as it grows in atmosphere and in sea. If there is a mass consentration, like planet, it will get more hits, and it will have shade on the Sun's side. And this fit's exactly on the Newton's gravity laws.
Shortly, the Gravity is like pressure, but you need enough connected atoms to make a difference between the random directions and the systematical direction of these collisions. This would mean that all particle size are influenced; like answered here by AnnaV; What is the smallest item for which gravity has been recorded or observed? But it would also explain how very small particles can flow in the air quite some time.