Background Consumption of sugar-sweetened beverages (SSBs) increases the risk of overweight and obesity. Taxing SSBs could decrease daily energy consumption and body weight. This model-based study evaluated the impact of a 20% SSB- sales tax on overweight and obesity in the context of Germany. Methods The population aged 15–79 years was modelled. Taxation was assumed to affect energy consumption via demand elasticities, which affected weight and BMI. Model-based analysis was performed to estimate the tax impact on BMI in different age, gender and income groups. Results Implementing a 20% SSB tax reduced energy consumption mainly in younger age groups, males, and those with low income. Taxation decreased the mean BMI in younger groups, with the largest decrease in those aged 20–29 years, while effects in groups 60 years or above were minimal. In absolute terms, taxation was estimated to avoid 1,028,000 (−3% relative reduction) overweight individuals and 479,000 obese individuals (−4%). Overweight decreased the most in males aged 20–29 years (408,000 fewer cases /−22%), the same applied for obesity (204,000/−22%). Conclusions An SSB tax could have significant impact on overweight and obesity, which could translate into substantial reductions of morbidity and mortality.