Lateral dimensions of III-V nanowires are known to affect the growth dynamics and crystal structure. Investigations into size effects have in the past relied on theoretical models and post growth observations, which only give a limited insight into the growth dynamics. Here we show the first experimental investigation into how nanowire diameter affects the growth dynamics by growing Au-seeded GaAs nanowires in an environmental transmission electron microscope. This was done by recording videos of nanowires during growth and analysing the Ga-limited incubation time and As-limited step-flow time. Our data show that the incubation time is stable across the investigated diameter range aside from a sharp increase for the smallest diameter, whereas the step-flow time is observed to steadily increase across the diameter range. We show using a simple model that this can be explained by the increasing vapour pressure in the droplet. In addition to the existing understanding of nanowire growth at small dimensions being limited by nucleation this work provides experimental evidence that growth is also limited by the inability to finish the step-flow process.