I addressed this point in an older answer about Spartan male citizen bodies - I'll copy the relevant section here:

Several ancient sources were very interested in the appearance of Spartans, but they mainly commented on their long hair and the ways in which their uniform equipment increased the terror they inspired in battle. There is little focus on Spartan men's bodies. The only thing we get is the suggestion that Spartiates were taller than other Greeks:

Whether [the mythical lawgiver Lykourgos] succeeded in populating Sparta with a race of men remarkable for their size and strength, anyone who chooses may judge for himself.

-- Xenophon, Constitution of the Spartans 1.10

However, Xenophon's point here is not to describe the great bodies they acquired through training, but to affirm the success of their eugenic practices. Xenophon's claim comes after a description of the way in which Spartan laws ensured that women were healthy and vigorous, and would sleep with healthy and vigorous men, so that their children would be naturally strong. The thinking behind these practices is explicit in an anecdote Plutarch gives about king Archidamos:

According to Theophrastos, Archidamos was fined by the ephors for marrying a short woman, "For she will bear us," they said, "not kings, but kinglets."

-- Plutarch, Life of Agesilaos 2.3

The reason why the saying of the ephors is preserved is that it turned out they were right: Archidamos' younger son, the eventual king Agesilaos II, was short and slight, and also lame in one leg. We should conclude from this that the Spartans may have done what they could through social engineering to produce tall and healthy citizens, but their control was not absolute, their science not particularly informed, and their results therefore mixed at best.

It is relevant to note here that we can't simply assume the Spartans' alleged greater height was due to the fact that their diet contained a lot more meat than that of other Greeks. We know this is true for Spartan adults, but no source tells us whether children would have eaten the infamous "black broth" (pork blood stew) while growing up. The only thing we hear about the diet of Spartiate boys is that they were deliberately underfed, to accustom them to hardship and encourage them to exercise cunning to supplement their diet. This ought to have resulted in Spartans being shorter, not taller, than Greeks whose diet was not so restricted during crucial periods of physical growth. On the other hand, our perception of the issue is warped by the fact that other Greek citizen bodies included many poor people who would have suffered routine malnutrition. The Spartan citizen body consisted only of leisure-class landowners; being rich was a requirement for citizenship. In other words, the average Spartan citizen boy - even if he was structurally underfed - may have had a more nutritious diet than the average Greek citizen growing up.