1. Informed consent before study-related activity

2. Individuals between the ages of 18 and 60 who meet Diagnostic and Statistical Manual of Mental Disorders, 5th Edition (DSM-5) criteria for MDD

3. Overweight (i.e. BMI ≥ 25 kg/m2)

4. Below-average (i.e. >1 SD below norm) performance in the Trail Making Test-B (TMTB)

1. Current, or in the past 4 weeks, treatment with other oral hypoglycemic agents and/or insulin

2. Diagnosis of possible or probable Alzheimer's Disease, Mild Cognitive Impairment, or any other dementia

3. History of neurological disorder, or evidence of neurologic or other physical illness that could produce cognitive deterioration

4. Severe mood episode, defined as a Hamilton Depression Rating Scale (HAMD-17) score of >23

5. Actively suicidal or evaluated as being a suicide risk (operationalized as a score of ≥3 on HAMD-17 suicide item and/or by clinical assessment).

6. Substance use disorder within 3 months before screening or a positive baseline toxicology screen

7. DSM-5 diagnosis of obsessive compulsive disorder, posttraumatic stress disorder (current or within the last year), or borderline personality disorder as assessed by a study investigator

8. Presence of absolute or relative contraindication to semaglutide (e.g. hypersensitivity to semaglutide, hepatic impairment, renal impairment with chronic kidney disease stage 3 and above, personal or familial history of medullary thyroid cancer or Multiple Endocrine Neoplasia syndrome type 2)

9. History of diabetic retinopathy

10. History of pancreatitis or pancreatic cancer

11. Presence of clinically unstable general medical illness

12. Pregnancy or breastfeeding women