Yeah, Hampden-Sydney College does provide scholarships based on merit. Here are some of them:

Allan Scholarship
Total Worth: $30,000 per year
Eligibility: $30,000 per year
Minimum Criteria: SAT: 1450, ACT: 32 and a 4.0+ grade-point average and a class rank in the top 5%.
Separate application needed: No

Venable Scholarship
Total Worth: $25,000 per year
Eligibility: $25,000 per year
Minimum Criteria: SAT: 1400, ACT: 30 and a 4.0 grade-point average and a class rank in the top 10%.
Separate application needed: No

Patrick Henry Scholarship
Total Worth: $21,000 per year
Eligibility: $21,000 per year
Minimum Criteria: SAT: 1300, ACT: 28 and a 3.8 grade-point average and a class rank in the top 15%.
Separate application needed: No

Hampden-Sydney College provides aids at an average of 33456 per student meeting 79% of students need. 100% of students with need receive financial aid at an average of 29916 need-based grant. They also provide other scholarships including Eagle Scout Scholarship and Madison Scholarship.