The majority of speech summarization research has focused on extracting the most informative dialogue acts from recorded, archived data. However, a potential use case for speech summarization in the meetings domain is to facilitate a meeting in progress by providing the participants - whether they are attending in-person or remotely - with an indication of the most important parts of the discussion so far. This requires being able to determine whether a dialogue act is extract-worthy before the global meeting context is available. This paper introduces a novel method for weighting dialogue acts using only very limited local context, and shows that high summary precision is possible even when information about the meeting as a whole is lacking. A new evaluation framework consisting of weighted precision, recall and f-score is detailed, and the novel online summarization method is shown to significantly increase recall and f-score compared with a method using no contextual information.