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

Presidential Academic Scholarships
Minimum Criteria: Based on aademic peformance
Requirement for maintenance: maintain continuous full-time enrollment and satisfactory academic progress
Separate application needed: No

Stephen Joel Trachtenberg (SJT) Scholarship
Total Worth: full tuition and fees (beyond the DC Tag Program allowance), room and board and include a book allowance
Eligibility: full tuition and fees (beyond the DC Tag Program allowance), room and board and include a book allowance

Scottish Rite Scholarship
Total Worth: half of tuition costs
Eligibility: half of tuition costs
Minimum Criteria: Based on academic performance

George Washington University provides aids at an average of 46348 per student meeting 90% of students need. 98% of students with need receive financial aid at an average of 32167 need-based grant. They also provide other scholarships including Athletic Scholarship and ROTC Scholarship.