Establish a relationship between g and G.

Let us assume a body of mass 'm' kept on the surface of the Earth of mass 'M'. The gravitational force exerted on the object equal to its weight. It is given as

F = W = mg

here g is the acceleration due to gravity.

Now according to the Newton's Law of Gravitation the force between the body and Earth is given as

F' = GMm/R²

here R is the distance between the two, which in this case will be the radius of the Earth (as body is kept on its surface) and G is the Newton's Gravitational Constant.

Now the two forces F and F' are same physically and in magnitude, thus 

F = F'

or

mg = GMm/R²

or

the relation between g and G will be

g = GM / R²