Severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has caused a wide spectrum of diseases in the human population, from asymptomatic infections to death. It is important to study the host differences that may alter the pathogenesis of this virus. One clinical finding in coronavirus disease 2019 (COVID-19) patients is that people with obesity or diabetes are at increased risk of severe illness from SARS-CoV-2 infection. We used a high-fat diet model in mice to study the effects of obesity and type 2 diabetes on SARS-CoV-2 infection as well as how these comorbidities alter the response to vaccination. We find that diabetic/obese mice have increased disease after SARS-CoV-2 infection and they have slower clearance of the virus. We find that the lungs of these mice have increased neutrophils and that removing these neutrophils protects diabetic/obese mice from disease. This demonstrates why these diseases have increased risk of severe disease and suggests specific interventions upon infection.