In line with aspects of the H2020 Feed-a-Gene project (grant agreement no. 633531) aiming to understand the genetic relationship between feed efficiency and robustness, we analysed the influence of mice feeding restriction on their offspring birth weights (BW) in two lines divergently selected for birth weight environmental variability. A total of 120 females (four full-sib females from 10 random different litters of the 12, 13 and 14 generations of selection) were chosen within high and low selected lines and split in four groups of feeding type combining restriction or not in two periods: from weaning at 21 to 77 days, and one week before mating to the 2nd parturition. Restriction consisted of feeding with 75, 90 and 85% of ad libitum consumed feed in the respective three studied generations. The data included 158 litters with 1,275 BW and 4,093 animals in the pedigree. A heteroscedastic model (using ASReml Release 4.1 software) was fitted to ascertain the genetic and environmental factors affecting the BW mean and its residual variance. The model included the diet type of the dam (restricted or not during the growing period and during the reproductive period), its line, generation, litter size where it was born and its parity, as well as the litter size of the progeny and its sex; including also all diet, line and generation interactions. The line (lower BW for the low variability line), and the generation effect for the progeny of dams restricted both during the growing and the reproductive period had significant effects on the progeny BW. Whereas the sex, the interaction diet-line (in dam pregnancy period) and the dam genetic effect have had effect on the BW variability. The interaction dietline produced a decrease in environmental variability of 5 and 18% in low and high variability lines respectively. It seems that selection for BW variability has conferred a lower sensitivity of the dams to the environmental conditions, which could be interpreted as higher robustness.