Spartans were really tough about bringing up their future warriors. The fact that they threw weak babies over a mountain is known from the ancient Greek writer, Plutarch. But modern scientists believe that it’s either not true or it was just a one-time thing, not a regular phenomenon.
In ancient Sparta, there really was a tradition to throw people into pits, but it was only done to prisoners and criminals. Recent anthropological studies showed that the remains belonged to men aged 18 to 35. There were also other bones found, but there was no trace of newborn babies. So today, there is no evidence that Spartans killed weak babies.