Obesity is a non-communicable disease that has a major impact on people’s health, increasing the risk of other chronic diseases such as diabetes, hypertension, and cardiovascular problems. Usually, the nutritional status of the population is determined by the body mass index (BMI) applied on a population sample via a national health survey (NHS), whose results are extrapolated. Except for highlighted cases such as the United States of America, these NHSs are infrequently carried out with different sampling methodologies. The outcomes are sparse and low-quality data, which complicate the estimation and forecasting of the population’s BMI distribution. In this work, this problem is addressed by considering the case of Chile, one of the countries with the highest prevalence of obesity, with an NHS every 7 years. Our approach proposes a maximum entropy optimization model to estimate the probability transition between different nutritional states, considering age and sex, which is based on the analogy with the determination of the origin-destination trip matrix used in the transport setting. The obtained results show that for the year 2024, there will be an increase of 798,898 (35%) and 758,124 (30%) men and women respectively, with overweight and obesity.