Obesity is a severe health problem linked to an increased risk of comorbidity and mortality and its etiopathogenesis includes genetic, epigenetic, microbiota composition, and environmental factors, such as dietary habits. The olfactory system plays an important role in controlling food intake and meal size, influencing body weight and energy balance. This study aims to identify the connection between olfactory function and clinical and nutritional aspects related to weight excess in a group of 68 patients with overweight or obesity. All participants underwent the evaluation of olfactory function, anthropometric data (weight, height, BMI, waist circumference), clinical data (hypertension, disglycemia, dyslipidemia, metabolic syndrome), and adherence to the Mediterranean diet (Mediterranean Diet Score). A fourth-generation artificial neural network data mining approach was used to uncover trends and subtle associations between variables. Olfactory tests showed that 65% of patients presented hyposmia. A negative correlation was found between olfactory scores and systolic blood pressure, fasting plasma glucose, and triglycerides levels, but a positive correlation was found between olfactory scores and the Mediterranean diet score. The methodology of artificial neural networks and the semantic connectivity map “Auto-Contractive Map” highlighted the underlying scheme of the connections between the variables considered. In particular, hyposmia was linked to obesity and related metabolic alterations and the male sex. The female sex was connected with normosmia, higher adherence to the Mediterranean diet, and normal values of blood pressure, lipids, and glucose levels. These results highlight an inverse correlation between olfactory skills and BMI and show that a normosmic condition, probably because of greater adherence to the Mediterranean diet, seems to protect not only from an excessive increase in body weight but also from associated pathological conditions such as hypertension and metabolic syndrome.