This aggregator may prove helpful to you: Merit Aid by Institution – College Transitions
It indicates the percentage of students without need that received merit aid and what the average merit award was. Double-check the information for any interested schools in their Common Data Sets. And if a school is not listed here, refer to the Common Data Set, section H2, I believe.
But for the three schools you mentioned:
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Case Western: 41%, average $26,072
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Wake Forest: 30%, average $32,196
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William & Mary: 6%, average $9,065