Let's talk about varying G
  It is possible that fundamental constants may not be constant at all. There
is a generally accepted view that one can only talk about variations of
dimensionless quantities, such as the fine structure constant $\alpha_{\rm
e}\equiv e^2/4\pi\epsilon_0\hbar c$. However, constraints on the strength of
gravity tend to focus on G itself, which is problematic. We stress that G needs
to be multiplied by the square of a mass, and hence, for example, one should be
constraining $\alpha_{\rm g}\equiv G m_{\rm p}^2/\hbar c$, where $m_{\rm p}$ is
the proton mass. Failure to focus on such dimensionless quantities makes it
difficult to interpret the physical dependence of constraints on the variation
of G in many published studies. A thought experiment involving talking to
observers in another universe about the values of physical constants may be
useful for distinguishing what is genuinely measurable from what is merely part
of our particular system of units.
