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

Gonzaga Merit Scholarships
Total Worth: $9,000 to $22,000 per year
Eligibility: $9,000 to $22,000 per year
Minimum Criteria: difficulty of curriculum, grade point average, SAT or ACT test scores
Requirement for maintenance: enrolled in 12+ credits each term, and maintain good academic standing to guarantee continuous scholarship
Separate application needed: No

Joseph M. Cataldo, S.J. Scholarships
Total Worth: $5000/year
Eligibility: $5000/year
Minimum Criteria: Minimum unweighted GPA of 3.75 ; Minimum test scores of 1310 SAT OR 28 ACT
Separate application needed: Yes
Application deadline: February 1

Dauna Leigh Bauer Scholarships
Total Worth: $2000/year
Eligibility: $2000/year
Minimum Criteria: Minimum unweighted GPA of 3.75 ; Minimum test scores of 1310 SAT OR 28 ACT
Separate application needed: Yes
Application deadline: February 1

Gonzaga University provides aids at an average of 27736 per student meeting 82% of students need. 100% of students with need receive financial aid at an average of 21414 need-based grant. They also provide other scholarships including Daniel G. Brajcich Scholarships and Joseph C. Metcalfe Scholarships.