Perceptual decision-making in a dynamic environment requires two integration processes: integration of sensory evidence from multiple modalities to form a coherent representation of the environment, and integration of evidence across time to accurately make a decision. Only recently studies started to unravel how evidence from two modalities is accumulated across time to form a perceptual decision. One important question is whether information from individual senses contributes equally to multisensory decisions. We designed a new psychophysical task that measures how visual and auditory evidence is weighted across time. Participants were asked to discriminate between two visual gratings, and/or two sounds presented to the right and left ear based on respectively contrast and loudness. We varied the evidence, i.e., the contrast of the gratings and amplitude of the sound, over time. Results showed a significant increase in performance accuracy on multisensory trials compared to unisensory trials, indicating that discriminating between two sources is improved when multisensory information is available. Furthermore, we found that early evidence contributed most to sensory decisions. Weighting of unisensory information during audiovisual decision-making dynamically changed over time. A first epoch was characterized by both visual and auditory weighting, during the second epoch vision dominated and the third epoch finalized the weighting profile with auditory dominance. Our results suggest that during our task multisensory improvement is generated by a mechanism that requires cross-modal interactions but also dynamically evokes dominance switching.