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

Heritage Society Scholarship
Total Worth: $15,000
Eligibility: $15,000
Minimum Criteria: cumulative high school GPA of 3.5
Separate application needed: No

Presidential Scholarship
Total Worth: $12,000
Eligibility: $12,000
Minimum Criteria: cumulative high school GPA of 3.8
Separate application needed: No

Honors Scholarship
Total Worth: $10,000
Eligibility: $10,000
Minimum Criteria: cumulative high school GPA of 3.3
Separate application needed: No

University of Dubuque provides aids at an average of 31338 per student meeting 85% of students need. 100% of students with need receive financial aid at an average of 24826 need-based grant. They also provide other scholarships including ROTC Service Award (Contracted Cadets) and Alumni Grant.