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

Merit Scholarship
Total Worth: Instate: $1,000-5,000, Out-of-State: $5,000-9,000
Eligibility: Instate: $1,000-5,000, Out-of-State: $5,000-9,000
Minimum Criteria: Based on academic performance
Separate application needed: No
Application deadline: February 1

Washington Scholarship
Total Worth: Full scholarship for instate tuition and fees, room and board
Eligibility: Full scholarship for instate tuition and fees, room and board
Separate application needed: No
Application deadline: November 15

Alvey Scholarship
Total Worth: Full scholarship for out of state tuition and fees, room and board.
Eligibility: Full scholarship for out of state tuition and fees, room and board.
Separate application needed: No
Application deadline: November 15

University of Mary Washington provides aids at an average of 9573 per student meeting 44% of students need. 99% of students with need receive financial aid at an average of 3603 need-based grant. They also provide other scholarships including Jepson Scholarship and Dorsey Scholarship.