Fitness trackers are increasingly popular. The data they collect provides substantial benefits to their users, but it also creates privacy risks. In this work, we investigate how fitness-tracker users perceive the utility of the features they provide and the associated privacy-inference risks. We conduct a longitudinal study composed of a four-month period of fitness-tracker use (N = 227), followed by an online survey (N = 227) and interviews (N = 19). We assess the users' knowledge of concrete privacy threats that fitness-tracker users are exposed to (as demonstrated by previous work), possible privacy-preserving actions users can take, and perceptions of utility of the features provided by the fitness trackers. We study the potential for data minimization and the users' mental models of how the fitness tracking ecosystem works. Our findings show that the participants are aware that some types of information might be inferred from the data collected by the fitness trackers. For instance, the participants correctly guessed that sexual activity could be inferred from heart-rate data. However, the participants did not realize that also the non-physiological information could be inferred from the data. Our findings demonstrate a high potential for data minimization, either by processing data locally or by decreasing the temporal granularity of the data sent to the service provider. Furthermore, we identify the participants' lack of understanding and common misconceptions about how the Fitbit ecosystem works.