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

John M. Belk Scholarship
Total Worth: Comprehensive cost plus $3,000 special study stipends
Eligibility: Comprehensive cost plus $3,000 special study stipends
Minimum Criteria: Based on exceptional achievement and promise in academics, character, leadership, and service.

Charles Scholarship
Total Worth: Full cost of attendance
Eligibility: Full cost of attendance
Minimum Criteria: Based on records of academic and personal accomplishment

Norris Scholarship
Total Worth: Full comprehensive cost
Eligibility: Full comprehensive cost
Minimum Criteria: Based on excellent leadership qualities

Davidson College provides aids at an average of 47564 per student meeting 100% of students need. 100% of students with need receive financial aid at an average of 43859 need-based grant. They also provide other scholarships including Lowell L. Bryan Scholarship and Charles Scholarship.