This paper presents an analysis of the relation between effort and gravitational stiffness, two physical measures that depend on the configuration of the robot. It is shown that whenever the gravitational stiffness is maximized, the effort is indirectly minimized. A minimum effort attractor that controls the gravitational stiffness is presented. This attractor together with an attractor to zero joint momentum guarantee balance maintenance. The novel implementation of the attractor-based Whole-body Motion Control (WBMC) System is experimentally tested: first with simple models, and finally with the full-body humanoid robot COMAN in a physical simulation.