Sorry about the misguidance to that google search. Well perhaps I should just direct you to the university where I teach instead:

"The laser-ranging data are used to test whether gravitational self-energy obeys the Equivalence Principle, because the Earth's mass has a 4 ? 10-10 contribution from gravitational binding energy...."
http://www.npl.washington.edu/eotwash/equivtst.html

Simply put:
weight = mass x acceleration due to gravity

The more gravity ... the more acceleration.
The more acceleration ... the more earth weights.

DA Morgan