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

Presidential Scholarship
Total Worth: Full tuition
Eligibility: Full tuition
Minimum Criteria: GPA: 3.75, ACT: 27, SAT: 1280, rank in the top 20% of your high school graduating class.
Requirement for maintenance: 3.5 GPA
Application deadline: January 8

Webster Gold Scholarship
Total Worth: $18,000
Eligibility: $18,000
Requirement for maintenance: 3.0 GPA

Webster Blue Scholarship
Total Worth: $16,000
Eligibility: $16,000
Requirement for maintenance: 3.0 GPA

Webster University provides aids at an average of 27407 per student meeting 69% of students need. 100% of students with need receive financial aid at an average of 8045 need-based grant. They also provide other scholarships including Leadership Scholarship and Girls State Scholarship.