How much weight do essays, ec, and recs actually carry?

In my opinion they cannot make up for less than optimal grades and stats. What they do is give you an opportunity to tell about yourself and differentiate yourself from others in similar academic circumstances. They make the most difference on the margins. If you are on the margin academically for a school the ECs, Rec and Essays may make a difference. Since nearly everyone who applies to very selective schools is on the margin so to speak (most applicants are academically qualified) these will be the differentiator.