I hate stories like this. This is an observation - Weight correlates with school performance. This is a hypothesis:
The new data suggest that the thresholds to maximize a child’s health seem to be higher, which means that many fetuses might benefit by staying longer in the womb, where they typically add at least a quarter-pound per week.
It is one possible explanation for the observation. It could also be that there is a correlation between genetic factors impacting baby weight and school performance. It could be that parents with more money have better pre-birth healthcare alternatives and so have heavier babies. It could be that low weight births due to maternal health issues correlate or any number of other things. All of those other possible hypotheses are ignored and one completely untested hypothesis is presented as fact. Engineers who do that around here find themselves out of a job, not getting articles in the NY Times.
It's an interesting observation though.