Here are en.Wikipedia, a UK Government site, and a training programme from the US CDC about their Public Health Prevention Service which talks about Obesity.
http://en.m.wikipedia.org/wiki/Public_health
https://www.gov.uk/government/topics/public-health
http://www.cdc.gov/phps/More.html
All three of these reputable sources specifically mention obesity as a public health problem.
What source are you using for your more restricted meaning of the term?