The introduction of highly effective anti-obesity drugs, such as Wegovy, has prompted debate over Medicare's prohibition on coverage of such products. In this study, we estimated the costs of allowing Medicare coverage of anti-obesity medications. Our analysis incorporated data on drug costs, real-world adherence rates, and potential changes to other health care spending. Using Medicare claims, we also documented beneficiaries' eligibility for nearly identical products approved for different indications. Assuming that anti-obesity drugs were covered in 2025 and that 5 percent or 10 percent of newly eligible patients were prescribed one, annual Part D costs were estimated to increase by $3.1 billion or $6.1 billion, respectively. The marginal costs of this policy could fall by as much as 62.5 percent from baseline estimates if products were approved for additional indications in coming years because these additional conditions are common among people with obesity. This would increase Medicare spending but would occur regardless of a policy change. Longer-term estimates come with significant uncertainty about utilization and price changes, but these results are consistent with this policy change likely increasing Medicare costs by the low to middle tens of billions of dollars over ten years.