The gravitational constant G, is a scaling factor used in all modern and classical theories of gravity. The problem with "big G" is that it cannot be expressed in a relationship to any other known constants in physics. This forces us puny humans of the 21st century to measure big G experimentally. Because gravity is both universal for all mass, and its so weak relative to other forces, experimentally measuring it is very difficult even for the most expensive and sensitive lab equipment. There is no agreed-upon method for measuring G, and the results of measurements performed all over the world often disagree on the value to as much as 0.6% error.

If sixth tenths of a percent seems "small" to you, consider this fact: The distance from the earth to the moon is known to an experimental error of 3 centimeters. So an error as large as 0.6% in a fundamental constant of nature, in the year 2015, is an embarrassment.

In the following linked article, you can follow various lab teams from the USA, Europe, and Russia, as they devise ever more clever methods of measuring G, in their collective battle to find its true value.

http://www.npl.washington.edu/eotwash/bigG