Background Body mass index ^†Deceased. (BMI) is a risk factor for heart failure with preserved ejection fraction (HFpEF). Design We investigated the threshold BMI and sex-specific waist circumference associated with increased HFpEF incidence in the SCReening Evaluation of the Evolution of New Heart Failure (SCREEN-HF) study, a cohort study of a community-based population at increased cardiovascular disease risk. Methods Inclusion criteria were age ≥60 years with one or more of self-reported hypertension, diabetes, heart disease, abnormal heart rhythm, cerebrovascular disease or renal impairment. Exclusion criteria were known heart failure, ejection fraction <50% or more than mild valve abnormality. Among 3847 SCREEN-HF participants, 73 were diagnosed with HFpEF at a median of 4.5 (interquartile range: 2.9–5.5) years after enrolment. Results HFpEF incidence rates were higher for BMI ≥27.5 kg/m² than for BMI < 25 kg/m², and for waist circumference >100 cm (men) or > 90 cm (women) than for waist circumference ≤94 cm (men) or ≤ 83 cm (women) in Poisson regression analysis. Semiparametric proportional hazards analyses confirmed these BMI and waist circumference thresholds, and exceeding these thresholds was associated with an attributable risk of HFpEF of 44–49%. Conclusions Both central obesity and overweight were associated with increased HFpEF incidence. Although a randomised trial of weight control would be necessary to establish a causal relationship between obesity/overweight and HFpEF incidence, these data suggest that maintenance of BMI and waist circumference below these thresholds in a community similar to that of the SCREEN-HF cohort may reduce the HFpEF incidence rate by as much as 50%.