During spoken language comprehension, listeners make use of both knowledge-based and signal-based sources of information, but little is known about how cues from these distinct levels of representational hierarchy are weighted and integrated online. In an eye-tracking experiment using the visual world paradigm, we investigated the flexible weighting and integration of morphosyntactic gender marking (a knowledge-based cue) and contextual speech rate (a signal-based cue). We observed that participants used the morphosyntactic cue immediately to make predictions about upcoming referents, even in the presence of uncertainty about the cue's reliability. Moreover, we found speech rate normalization effects in participants' gaze patterns even in the presence of preceding morphosyntactic information. These results demonstrate that cues are weighted and integrated flexibly online, rather than adhering to a strict hierarchy. We further found rate normalization effects in the looking behavior of participants who showed a strong behavioral preference for the morphosyntactic gender cue. This indicates that rate normalization effects are robust and potentially automatic. We discuss these results in light of theories of cue integration and the two-stage model of acoustic context effects.