I don't think the mechanism is a direct biological signaling of the baby's sex to tell the woman to produce fattier milk. It seems more plausible to me that we

I don't think the mechanism is a direct biological signaling of the baby's sex to tell the woman to produce fattier milk. It seems more plausible to me that wealthier families value boys a lot more - you see this tendency everywhere. This causes mothers to value their male children disproportionately, and the social feedback she gets probably affects her hormones as well, which would cause the milk to vary. So you see the large difference in wealthier women's milk for boys and girls, whereas the difference in poorer women's milk may not even be statistically significant. I think if you repeat this test on different circumstances where the child is valued or not, whether boy or girl, you will find similar results that remove the sex factor.