This study establishes the relationship between surgical volume and cost and quality outcomes, using patient-level clinical data from a national quality registry for bariatric surgery in Sweden. Data include patient characteristics with comorbidities, surgical and follow-up data for patients that underwent gastric bypass or gastric sleeve operations between 2007 and 2016 (52,703 patients in 51 hospitals). The relationships between surgical volume (annual number of bariatric procedures) and several patient-level outcomes were assessed using multilevel, mixed-effect regression models, controlling for patient characteristics and comorbidities. We found that hospitals with higher volumes had lower risk of intraoperative complications as well as complications within 30 days post-surgery (odds ratios per 100 procedures are 0.78 and 0.87, respectively, p<0.01). In addition, higher-volume hospitals had substantially shorter procedure time (17 min per 100 procedures, p<0.01) and length of stay (0.88 incidence-rate ratio per 100 procedures p<0.01). Our results support the claim that increased surgical volume significantly improves quality. Further, the results strongly suggest that increased volume leads to lower cost per surgery, by reducing cost drivers such as procedure time and length of stay.