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

Hathway Schlolarships-Honors Level
Total Worth: $1,680 per semester
Eligibility: $1,680 per semester
Minimum Criteria: 3.5 GPA and 25 ACT/1200 SAT

Rocky Mountain Scholars
Total Worth: 150% of resident tuition
Eligibility: 150% of resident tuition
Minimum Criteria: 1300+ SAT; 28+ ACT
Requirement for maintenance: maintain full-time continuous enrollment in Laramie campus courses (12 semester hours) during the Fall and Spring semesters each year but is not available to use during the Summer semester; Students must maintain a 3.0 cumulative GPA
Separate application needed: No

Rocky Mountain Scholars for International
Total Worth: $5,500
Eligibility: $5,500
Minimum Criteria: 3.4-4.0 GPA
Requirement for maintenance: Students must maintain full-time continuous enrollment in Laramie campus courses (12 semester hours) during the Fall and Spring semesters each year but is not available for use during the Summer semester; Students must maintain a 3.0 cumulative GPA
Separate application needed: No

University of Wyoming provides aids at an average of 10701 per student meeting 66% of students need. 98% of students with need receive financial aid at an average of 4977 need-based grant.