The objective of this work was to study the changes that, selecting for environmental variability of birth weight (BW), could bring to other interesting traits in livestock such as: survivability at weaning (SW), litter size (LS) and weaning weight (WW), their variability assessed from standard deviations of LS, standard deviation of WW (SDWW) and also the total litter weight at birth (TLBW) and total litter weight at weaning. Data were registered after eight generations of a divergent selection experiment for BW environmental variability in mice. Genetic parameters and phenotypic and genetic evolution were assessed using linear homoscedastic and heteroscedastic models in which the traits were attributed to the female, except BW and WW that were in some models also attributed to the pup. Genetic correlation between the trait and variability levels was −0.81 for LS and −0.33 for WW. Clear divergent phenotypic trends were observed between lines for LS, WW and SDWW. Although animals were heavier in the high line, TLBW and at weaning was greater in the low line. Despite the negative genetic correlation that was obtained, SDWW was also higher in the high line. Heritabilities were 0.21 and 0.06, respectively, for LS and SW. Both phenotypic and genetic trends showed clear superiority of the low line over the high line for these traits, but inferior for WW. Heteroscedastic model performed similar to the homoscedastic model when there was enough information. Considering LS and survival, the low line was preferred from a welfare point of view, but its superiority from the productivity perspective was not clear. Robustness seemed higher as shown by a low variation and having a benefit to the animal welfare, but this still remains unclear. It was concluded that low variation benefits the welfare of animals.