Yeah, University of Virginia does provide scholarships based on merit. Here are some of them:

Bayly-Tiffany Scholarship
Separate application needed: No

Chick-Fil-A Bowl Scholarship
Total Worth: Full or partial scholarship
Eligibility: Full or partial scholarship
Separate application needed: No

V. Thomas Forehand, Jr. Scholarship
Separate application needed: No

University of Virginia provides aids at an average of 28872 per student meeting 100% of students need. 100% of students with need receive financial aid at an average of 22612 need-based grant. They also provide other scholarships including George E. Hamovit Memorial Scholarship and Benjamin F. Thomas Scholarship.