It is true that in a recent past, the weigh ins of boys and even teenagers or young men as draftees or inductees were generally performed in the nude under regulations of the procedure, it was not an option.
in many medical forms, it was mentioned that the weigh-ins might be performed in the nude, so we were told to strip completely at draft physical examinations in front of the draft board commission for military service at 18 age, and same at the pre-induction military centers and same at exams for sports or summer camps, or we were told to remove our underwears at school since we were all already undressed in underwears when we entered in the exam room.
It could not be discussed because it was the common rule admitted by all adults, it was the same for boys and male teenagers under 18 age at least , sometimes more until 21 age, it was the same rule applied at hospitals, it was obvious that being weighted in just underwear would have given the same result but at that time it was not allowed to keep it, the nudity was required and that's all, it was not an issue to have boys and teenagers naked on a scale, to complain was useless, it would have been considered as a silly behaviour, and the hands might be on the sides, never crossed in front of genitals , and of course we might also remove our socks even if wearing them on a scale would have not changed the result., it was in the buff and not questionable !