I don't think the Common App essay is weighted more heavily than the supplement, or vice-versa. Admissions Directors are looking at both essays for clues to your character, personality, interests, maturity and love of learning. As college students spend about half their time in class, specifically, they are looking for students who are good role models, teachers and scholars outside of the classroom. As William Fitzsimmons has stated: http://thechoice.blogs.nytimes.com/2009/09/10/harvarddean-part1/
"Personal qualities and character provide the foundation upon which each admission rests. Harvard alumni/ae often report that the education they received from fellow classmates was a critically important component of their college experience. The education that takes place between roommates, in dining halls, classrooms, research groups, extracurricular activities, and in Harvards residential houses depends on selecting students who will reach out to others."