Background: Rare biallelic pathogenic mutations in PCSK1 (encoding proprotein convertase subtilisin/kexin type 1 [PC1/3]) cause early-onset obesity associated with various endocrinopathies. Setmelanotide has been approved for carriers of these biallelic mutations in the past 3 years. We aimed to perform a large-scale functional genomic study focusing on rare heterozygous variants of PCSK1 to decipher their putative impact on obesity risk. Methods: This case-control study included all participants with overweight and obesity (ie, cases) or healthy weight (ie, controls) from the RaDiO study of three community-based and one hospital-based cohort in France recruited between Jan 1, 1995, and Dec 31, 2000. In adults older than 18 years, healthy weight was defined as BMI of less than 25·0 kg/m2, overweight as 25·0–29·9 kg/m2, and obesity as 30·0 kg/m2 or higher. Participants with type 2 diabetes had fasting glucose of 7·0 mmol/L or higher or used treatment for hyperglycaemia (or both) and were negative for islet or insulin autoantibodies. Functional assessment of rare missense variants of PCSK1 was performed. Pathogenicity clusters of variants were determined with machine learning. The effect of each cluster of PCSK1 variants on obesity was assessed using the adjusted mixed-effects score test. Findings: All 13 coding exons of PCSK1 were sequenced in 9320 participants (including 7260 adults and 2060 children and adolescents) recruited from the RaDiO study. We detected 65 rare heterozygous PCSK1 variants, including four null variants and 61 missense variants that were analysed in vitro and clustered into five groups (A–E), according to enzymatic activity. Compared with the wild-type, 15 missense variants led to complete PC1/3 loss of function (group A; reference) and rare exome variant ensemble learner (REVEL) led to 15 (25%) false positives and four (7%) false negatives. Carrying complete loss-of-function or null PCSK1 variants was significantly associated with obesity (six [86%] of seven carriers vs 1518 [35%] of 4395 non-carriers; OR 9·3 [95% CI 1·5–177·4]; p=0·014) and higher BMI (32·0 kg/m2 [SD 9·3] in carriers vs 27·3 kg/m2 [6·5] in non-carriers; mean effect π 6·94 [SE 1·95]; p=0·00029). Clusters of PCSK1 variants with partial or neutral effect on PC1/3 activity did not have an effect on obesity or overweight and on BMI. Interpretation: Only carriers of heterozygous, null, or complete loss-of-function PCSK1 variants cause monogenic obesity and, therefore, might be eligible for setmelanotide. In silico tests were unable to accurately detect these variants, which suggests that in vitro assays are necessary to determine the variant pathogenicity for genetic diagnosis and precision medicine purposes. Funding: Agence Nationale de la Recherche, European Research Council, National Center for Precision Diabetic Medicine, European Regional Development Fund, Hauts-de-France Regional Council, and the European Metropolis of Lille.