Is it true that birth at high altitudes causes babies to weigh less?

Yes: There was one study showing a difference of about 3 ounces at birth. This isn't much. And the babies born at high altitude were not more likely to be born prematurely or have growth problems later in life.

Yes: Pregnancy at high altitudes (not "birth" at high altitudes) causes babies to weigh less than in pregnancies at low altitudes. The likely reason is that there is less oxygen in the air at high altitudes. Because the lower weight in these high-altitude babies is not caused by some serious medical condition, these high-altitude babies are probably just fine even with their lower weights.

Yes: Pregnancy at high altitudes is associated with lower birth weight, at least among women who are not genetically from areas that are adapted to very high altitudes. But that lower birth weight does not seem to be associated with any significant or lasting health risks.