This is a Phase IIb, global, randomized, parallel-group, double-blind, placebo-controlled, multicenter study to assess the efficacy and safety of 5 doses of AZD5004 compared with placebo, given once daily as an oral tablet or tablets for a duration of 36 weeks, in adults aged 18 years and above, who are living with obesity (BMI ≥ 30 kg/m2), or overweight (BMI ≥ 27 kg/m2) and have at least 1 weight-related comorbidity (Hypertension, Dyslipidemia or hyperlipidemia, CV disease and/or Obstructive sleep apnea). Approximately 304 participants will be randomized in the study. The dual primary endpoints are percent change in body weight from baseline at 26 weeks and the proportion of participants with weight loss ≥ 5% of baseline weight at 26 weeks.