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

Danforth Scholars Program
Total Worth: full or partial-tuition
Eligibility: full or partial-tuition
Requirement for maintenance: The scholarship is renewed each year for the duration of the degree program, provided the scholar progresses academically and upholds the high standards of character required of scholars.
Separate application needed: yes
Application deadline: January 2

Annika Rodriguez Scholars Program
Separate application needed: yes
Application deadline: January 2

John B. Ervin Scholars Program
Separate application needed: yes
Application deadline: January 2

Washington University in St. Louis provides aids at an average of 48169 per student meeting 100% of students need. 98% of students with need receive financial aid at an average of 45567 need-based grant. They also provide other scholarships including Nemerov Writing Scholars Program and Entrepreneurial Scholars Program.