Look to large redshift values with the Hubble telescope. Then do spectroscopy. Primary physical constants have not changed within visible time within experimental error - more than 14 significant figures for the hydrogen atom hyperfine transition. Look up the half-life of that spin flip, then Heisenberg for slop in the gears.
Terrestrial acceleration due to gravity is not a constant,
http://www.splung.com/content/sid/2/page/gravitation
http://www.typnet.net/Essays/EarthGrav.htm
bottom
Big G is a universal constant. It is the worst-measured physical constant, upon which all gravitation hinges. Even worse, the very modest accuracy values substantially diverge - and don't grow better over the years,
http://iopscience.iop.org/0957-0233/10/6/001
1999
http://www.nature.com/news/2010/100823/full/4661030a.html
2010