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

That is probably more the rule than the exception, at least in some states, since most state schools are not that selective and see sufficient distinction between applicants by GPA/rank/tests.

For example, the 22 CSUs in California using GPA/tests only outnumber the 9 UCs using holistic readings including essays (but not recommendations generally). All publics in Texas admit much of their classes by rank or rank/tests.