There are sensible reasons to be concerned about this form of state nannying. Firstly, as has been explained, the measurement is imprecise and brings up some false results, your child might be flabby and unfit but have an ok BMI and another child who is highly athletic might come up as obese (eg child in the paper). So one parent stays unaware another is stigmatised.
As an example, I used to compete in sport at a high level and my BMI looked pretty good but compared with some team-mates when the calipers came out (i.e. pinching the fat from the muscle) my actual body fat was fairly high, their weight was more muscle. Even this isn't the full story, some people are very slim but carry a lot of internal fat.
Secondly, it is human nature for children to talk about their weight and as they get older and the test is done in year 6, it may cause unwarranted anxiety. As I have posted my daughter is very tall and I knew that she would feel worried to be a lot heavier than her friends. I had never weighed her as I don't see what it adds. If you have a good body image then you can tell if your child is over or underweight.
IMO schools are for educating your child. A doctor's surgery is a good place for checking your child is a healthy weight with the parent there and in consultation. If it has to be at school then it should be a full health check with the parent invited in.
Yes, there is an obesity problem in all westernised nations where there is a fast food culture (interesting to see it now beginning in France). I'm for a tax on all fast food outlets for the burden they cause to the tax payer and for all the littering.
In case it should be relevant I do know my children's weights now and, according to the BMI tables they are in the healthy weight section and me too I should think.
To MM7777 why not see a nutritionist about your son? It is clearly concerning you and you might be missing something. When you think of the importance of good health, two or three sessions is a great investment.