The preweaning weight of kits has been related to their mortality during the suckling period. Selecting rabbit kits for individual body weight in the first days of life could be interesting; however, better knowledge of body weight’s heritability during the preweaning period is necessary to determine the opportune moment for selection. A total of 1696 growth records of kits from 81 females of the ITLEV2006 synthetic line were analysed in order to estimate the genetic and non-genetic parameters for individual body weight at birth as well as at 5, 7, 14, 21, 28, and 35 days of age. The estimates of heritability (h2) for individual weight were between low (0.11 at birth, 0.16 at 5 days, and 0.17 at 7 days) and moderate (0.21, 0.21, 0.24, and 0.21 at 14, 21, 28, and 35 days, respectively). Weight at birth showed a strong and positive genetic correlation with weight at 5 days (+0.79) and 7 days of age (+0.78), but the correlation was low for the rest of the weight measurements (+0.41, +0.49, +0.54, and +0.54 with weight at 14, 21, 28, and 35 days, respectively). Weight at 5 days and 7 days displayed strong and positive genetic correlations with the rest of the weight measurements (higher than +0.83). The values of the common litter effect (c2) were high, and they increased with age from 0.43 at birth to 0.66 at 35 days of age. The values of the maternal permanent effect (p2) were low compared to those of the common litter effect (c2), varying between 0.04 and 0.11. In conclusion, opting to select for body weight at 5 or 7 days of age would yield a greater response compared to selecting for birth weight. This approach would indirectly increase the kits’ weight at birth and at weaning, thereby reducing preweaning losses.