Children aged five and 11 are being tested
But ministers have stopped short of making the National Child Measurement Programme, introduced last year for five and 11-year-olds, compulsory.
The government set it up to help gather evidence so health chiefs can tailor programmes to overweight populations.
But it has been attacked as parents have not been given the data and less than half of pupils have taken part.
The government has included provisions in the Health and Social Care Bill, which has been published in Parliament, to ensure parents are told.
There will now be a consultation to decide what is the best way to inform parents after surveys showed they wanted to know.
To date, they have had to contact their local primary care trust to get the information - a process which parents had criticised as being cumbersome.
But the Department of Health said the scheme would not become mandatory as it was always meant to be voluntary because the government did not want to coerce children into it.
Coverage is also thought to be increasing after last year's results.
Figures from the first year of the programme showed that 538,400 children in both years were measured - about 48% of those eligible.
A report by the Association of Public Health Observatories said the results had to be treated with "considerable caution" as a result.
It said there was evidence to suggest higher rates of opting out among heavier children.
Health Minister Ben Bradshaw said giving the information to parents would help tackle the issue of obesity.
"Giving parents clear information about their child's weight is important way of engaging with families, and prompting a conversation about healthy lifestyles and weight issues within the home.
"This change to legislation is not about telling parents what to do, or lecturing them on how to raise their children, it is a way of supporting families to be healthy.
Tam Fry of the National Obesity Forum said: "It's a very good idea to give parents the results of the tests. But what do the parents do when they get the data?
"They should have a chart so they can plot the measurements in the future. That way they can keep track of how their child is getting on."