It has been known for long time that the measurements of G give differing results with differences between measurements larger than the measurement accuracy (see this and this). This suggests that there might be some new physics involved. In TGD framework the hierarchy of Planck constants heff=nh0, h=6h0 together with the condition that theory contains CP2 size scale R as only fundamental length scale, suggest the possibility that Newtons constant is given by G= R2/hbareff, where R replaces Planck length ( lP= (ℏ G1/2→ lP=R) and hbareff/h is in the range 106-107.
The spectrum of Newton' constant is consistent with Newton's equations if the scaling of hbareff inducing scaling G is accompanied by opposite scaling of M4 coordinates in M4× CP2: dark matter hierarchy would correspond to discrete hierarchy of scales given by breaking of scale invariance. In the special case heff=hgr=GMm/v0 quantum critical dynamics as gravitational fine structure constant (v0/c)/4π as coupling constant and it has no dependence of the value of G or masses M and m.
In this article I consider a possible interpretation for the finding of a Chinese research group measuring two different values of G differing by 47 ppm in terms of varying heff. Also a model for fountain effect of superfluidity as de-localization of wave function and increase of the maximal height of vertical orbit due to the change of the gravitational acceleration g at surface of Earth induced by a change of heff due to super-fluidity is discussed. Also Podkletnov effect is considered. TGD inspired theory of consciousness allows to speculate about levitation experiences possibly induced by the modification of Geff at the flux tubes for some part of the magnetic body accompanying biological body in TGD based quantum biology.
See the chapter About the Nottale's formula for hgr and the possibility that Planck length lP and CP2 length R are identical giving G= R2/ℏeff or the article Is the hierarchy of Planck constants behind the reported variation of Newton's constant?.