During the dependency period in mammals with parental care, offspring must develop the behavioral skills that allow them to forage independently and thus survive into early adulthood. Deep-diving Weddell seals (Leptonychotes weddellii) are a model species for research on diving physiology, yet previous studies lack a thorough investigation into the diving behavior of dependent pups when they first begin to enter the water. To capture fine-scale dive behavior during the dependency period, we deployed time-depth recorders (TDRs) on Weddell seal pups (n = 18) from the age of 1 week through 7 weeks, during the 2017 and 2019 breeding seasons in McMurdo Sound, Antarctica. Dive parameters were correlated with time of day, age, sex, and weaning status, to characterize diving behavior, and we used raw wet/dry data to determine which times of the day pups were most likely to be in the water. Pups made their deepest and longest dives and had the longest post-dive durations in the morning hours. Pups were in the water more during the late night and morning hours than in the afternoon. Whereas dive depth significantly increased with age, dive duration significantly increased with age and after weaning. Post-dive duration significantly decreased with age and after weaning. We discuss how dependent pups may prioritize the development of swimming and navigational abilities as opposed to building and practicing foraging skills.