As I said on another post, it is not just the lack of evidence for changes in constants in the past that makes it illogical to consider in science, but the lack of a mechanism that could cause such a change that makes it unscientific to even consider.
According Sheldrake Dirac suggested change of G 1*10-13 per year.
I don't see reason why constants couldn't change. Is it something like platonic ideas that existed before Big-bang? There was once no time, no space and yet value of constants had been fixed already and there was no change of G from the beginning? "On the beginning there was fixed Gravity constant".
Materialists should consider constants and physical laws as something secondary what is function of matter and caused by matter. Not sometning platonic a-priori without beginning and end what rules the world and what the blind matter follows.
Just questions.
Enjoy.