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

Miami University Scholarship Category 1
Total Worth: Half to full tuition per year ($18,000–$36,000 for Non-residents and $8,000–$16,000 for Ohio Residents Annually)
Eligibility: Half to full tuition per year ($18,000–$36,000 for Non-residents and $8,000–$16,000 for Ohio Residents Annually)
Minimum Criteria: ACT: 33+; SAT: 1450+; GPA: 3.50+
Requirement for maintenance: Maintain the academic requirements as stipulated in the financial aid award letter
Separate application needed: No

Miami University Scholarship Category 2
Total Worth: $11,000–$20,000 for Non-residents and $5,000–$12,000 for Ohio Residents Annually
Eligibility: $11,000–$20,000 for Non-residents and $5,000–$12,000 for Ohio Residents Annually
Minimum Criteria: ACT: 30-32; SAT: 1360–1440; GPA: 3.50+
Requirement for maintenance: Maintain the academic requirements as stipulated in the financial aid award letter
Separate application needed: No

Miami University Scholarship Category 3
Total Worth: $7,000–$15,000 for Non-residents and $2,000–$8,000 for Ohio Residents Annually
Eligibility: $7,000–$15,000 for Non-residents and $2,000–$8,000 for Ohio Residents Annually
Minimum Criteria: ACT: 28-29; SAT: 1300–1350; GPA: 3.50+
Requirement for maintenance: Maintain the academic requirements as stipulated in the financial aid award letter
Separate application needed: No

Miami University provides aids at an average of 14415 per student meeting 60% of students need. 97% of students with need receive financial aid at an average of 11417 need-based grant.