Weight
In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a "force" that results from the action of gravity on matter: it measures how strongly the force of gravity pulls on that matter. However, in most practical everyday situations the word "weight" is used when, strictly, "mass" is meant. For example, most people would say that an object "weighs one kilogram", even though the kilogram is a unit of mass.
Earth mass
The relative uncertainty of the geocentric gravitational constant is just , i.e. times smaller than the relative uncertainty for itself. 
For this reason and others, astronomers prefer to use the un-reduced "G" product, or mass ratios
(masses expressed in units of Earth mass or Solar mass) rather than mass in kilograms when referencing and comparing planetary objects.