I think I have realised why I don't want him to be weighed. It is the feeling that people are doing something so intrusive that the results have to be hidden from everyone present.
If the child is not told their weight, or height, and the other children are not told theirs either, and no one is allowed to even look at the scales apart from the data recorder - then that makes it feel rather sinister, and in fact makes a good case for not doing it imo.
Because something requiring that level of surreptition is something that should be done in private if necessary, on an individual basis.
I think the whole thing is horrible. I can see myself as an 11yo asking 'well what do I weigh' and being met with a horrified response of 'I cannot tell you that'.
It is condescending and nasty...it places the child within a discourse to which they have no access.
Would you like to be weighed in a line at work with your colleagues? No? Then don't make children take part in that.
btw nit nurse was always rather fun imo, but I think given my own misgivings about weighing, I probably should not be hankering for a return of that system either 
except nits affect everyone
weight is individual