Background Dementia and obesity are increasingly important public health issues. Obesity in middle age has been proposed to lead to dementia in old age. We investigated the association between BMI and risk of dementia. Methods For this retrospective cohort study, we used a cohort of 1?958?191 individuals derived from the United Kingdom Clinical Practice Research Datalink (CPRD) which included people aged 40 years or older in whom BMI was recorded between 1992 and 2007. Follow-up was until the practice's final data collection date, patient death or transfer out of practice, or first record of dementia (whichever occurred first). People with a previous record of dementia were excluded. We used Poisson regression to calculate incidence rates of dementia for each BMI category. Findings Our cohort of 1?958?191 people from UK general practices had a median age at baseline of 55 years (IQR 45–66) and a median follow-up of 9·1 years (IQR 6·3–12·6). Dementia occurred in 45?507 people, at a rate of 2·4 cases per 1000 person-years. Compared with people of a healthy weight, underweight people (BMI <20 kg/m2) had a 34% higher (95% CI 29–38) risk of dementia. Furthermore, the incidence of dementia continued to fall for every increasing BMI category, with very obese people (BMI >40 kg/m2) having a 29% lower (95% CI 22–36) dementia risk than people of a healthy weight. These patterns persisted throughout two decades of follow-up, after adjustment for potential confounders and allowance for the J-shape association of BMI with mortality. Interpretation Being underweight in middle age and old age carries an increased risk of dementia over two decades. Our results contradict the hypothesis that obesity in middle age could increase the risk of dementia in old age. The reasons for and public health consequences of these findings need further investigation.