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

OHIO Success Scholarship
Total Worth: $1,000–$7,000 per year
Eligibility: $1,000–$7,000 per year
Minimum Criteria: Minimum ACT composite score of 24 (or a comparable SAT score)
Separate application needed: No
Application deadline: Priority Deadline: December 1

OHIO Premier Scholarship
Total Worth: Up to full in-state tuition
Eligibility: Up to full in-state tuition
Separate application needed: No
Application deadline: Priority Deadline: December 1

The Manasseh Cutler Scholars Program
Total Worth: minimum of $92,000 across four years
Eligibility: minimum of $92,000 across four years
Minimum Criteria: Academically motivated and driven to explore the social and political impact of their intellectual interests
Separate application needed: No
Application deadline: Priority Deadline: December 1

Ohio University provides aids at an average of 9672 per student meeting 56% of students need. 100% of students with need receive financial aid at an average of 6847 need-based grant. They also provide other scholarships including Templeton Scholars Program and Harry and Ruth Rankin Scholarship Program.