The structure of the cumulative food intake (CFI) curve has been associated with obesity and eating disorders. Scales that record the weight loss of a plate from which a subject eats food are used for capturing this curve; however, their measurements are contaminated by additive noise and are distorted by certain types of artifacts. This paper presents an algorithm for automatically processing continuous in-meal weight measurements in order to extract the clean CFI curve and in-meal eating indicators, such as total food intake and food intake rate. The algorithm relies on the representation of the weight-time series by a string of symbols that correspond to events such as bites or food additions. A context-free grammar is next used to model a meal as a sequence of such events. The selection of the most likely parse tree is finally used to determine the predicted eating sequence. The algorithm is evaluated on a dataset of 113 meals collected using the Mandometer, a scale that continuously samples plate weight during eating. We evaluate the effectiveness for seven indicators and for bite-instance detection. We compare our approach with three state-of-the-art algorithms, and achieve the lowest error rates for most indicators (24 g for total meal weight). The proposed algorithm extracts the parameters of the CFI curve automatically, eliminating the need for manual data processing, and thus facilitating large-scale studies of eating behavior.