I’ve been curious about this for a while too, so I just went through the 2014-15 Common Data Set.
It looks like out of a cohort of 6,428 full-time freshmen in that class, 1,736 of those eligible for need-based financial aid also received non-need based scholarship or grant aid. Another 1,653 students with no demonstrated financial need were awarded non-need-based aid (excluding athletic awards and tuition benefits).
Assuming I’m using the right numbers and extrapolating correctly (a big assumption), it looks like @Atlanta68 is correct, that approximately 52% of students (3,389 out of 6,428) are receiving some form of non-need-based, the bulk of which I’m assuming is the automatic “merit” aid.
In case anybody is interested, the average amount of institutional non-need-based aid was $12,186. Keep in mind that dollar amount reflects both in-state and out-of-state awards and full and partial tuition awards. If somebody wants to go back and parse the in-state vs. out-of-state enrollment numbers to come up with a formula, they might be able to reveal more information about what percentage is receiving the Presidential or higher, both in-state and out-of-state.