Every time these threads come up I want to bang my head repeatedly on a hard surface. I was a school nurse for a while and as such was part of a School Health Team that carried out growth and health assessments and monitoring in schools.
Schools don't weigh and measure children - School Health Teams do.
They don't give the child their measurements or (IME) make any comment about their height and weight. It's presented as 'we want to see how you are growing'.
The eye tests carried out are very basic and are no substitute for a proper assesment and eye test by a qualified optician, but they are a starting point and can be an early discovery tool for squints and short or long sightedness.
The hearing test is quite simple but again can be an indicator for further assessment.
All results were collated by the School Health Team staff and then those that were in any way out of the ordinary (ie underweight, overweight, poor vision or hearing) were passed to a qualified nurse for further intervention. This may have meant a return visit to the school to see the child/school staff to see if there were any other concerns about health, or a phone call to the parent to see if they had any worries about their child.
Often concerns with growth (especially obesity) could allow a parent to access services such as a MEND programme, or a dietitian or paediatric referral, where they hadn't previously known how to access them. The parent may have had a niggling worry about hearing or vision but again not known how to proceed further.
I think many MNers that post here forget that not all parents are as switched on as them, or as educated and informed as them. Some really do benefit and appreciate interventions from health professionals with issues flagged up at school screening.
All that said, I do think it is vitally important that parents can choose to opt out of screening, but I would hope that those that do are well informed as to just what they are opting out of. The OPs health forms are naughty in that they are implying that screening will be carried out regardless, which is wrong.
We actually amended our information and consent forms for parents so that they had to actually tick each box for the screening they consented to, ie height, weight, vision and hearing. That way we could be sure they had fully consented to all parts of the screening process.