Acidic corrosion in industrial environments represents a serious threat that requires an active prevention and management strategy. In this context, weak acids can create a severe corrosion environment for metallic surfaces, sometimes exceeding the severity observed in strongly acidic solutions under similar conditions. While most of the research efforts of the last decades in the field of the predictive modeling of acidic corrosion have been focused on the specific case of sweet corrosion caused by carbonic acid, the goal of this work is to describe and validate a predictive model to be used as a more transversal tool for acidic corrosion. The model, called the Tafel–Piontelli model, leverages Tafel law to mechanistically describe the electrochemical behavior of carbon steel in acidic aqueous environments. Two different acids, acetic and valeric, were used to experimentally evaluate the performance of the model in weakly acidic solutions, varying the pH and the temperature conditions. Potentiodynamic polarization tests and mass loss tests were performed, allowing us to assess the kinetic parameters (the Tafel slope and the exchange current density of the cathodic and anodic reactions) and corrosion rates of the corrosion process. The promising results suggest that the Tafel–Piontelli model is able to adapt to different scenarios and its intrinsically theoretical nature allows us to extend its predictions outside the range of experimental conditions used to validate it.