The Roman army certainly had a minimum height requirement which exceeded the average height of the population as a whole. A story from a Talmudic
Midrash, dating to the Roman period, makes this point:
There is a case of a man who
conscripted recruits. A man came to
conscript someone’s son. [The father] said: look at my son . . . how
tall he is! His mother said: look at our son, how tall he is. The
[recruiter] answered: in your eyes . . . he is tall. I do not know. Let us
see whether he is tall. They measured [him] and he proved to be [too]
small and was rejected.14
...
It is not surprising to see such forced labor referred to by the
provincials in their literature: when the Mishnah mentions “idolworshipers” (gilulim), i.e.,
Romans, carrying off Jews; it probably refers
to conscription to corvée labor, which would include service as
porters.301 St. Matthew, has Jesus say: “whoever impresses (angareusei)
you to go one mile, go with him two miles.” Whether or not this
represents Jesus’ actual words, the Greek uses the technical word
for corvée labor, as well as a loan-word from Latin to mean “mile”
(milion).302 In first century Palestine, a Latin loan-word in such a context strongly suggests the “whoever” in this case represents a military officer. "
(THE LOGISTICS OF
THE ROMAN ARMY AT
WAR (264 B.C. - A.D. 235)
JONATHAN P. ROTH)
http://www.legioxxirapax.com/zasoby/The_Logistics_of_the_Roman_Army_at_War_(264BC_-_235AD).pdf