The same public health/expense excuse can be made to monitor just about every aspect of your private life, if the intent is there. 'Public health costs' have become the Interstate Commerce Clause of the war on privacy and private property--carte blanche.
Once the laws and monitoring systems are in place, the associated laws become a device for generating revenue through fines for violations. Violations are reported by computers, what a regulatory wet dream! Kind of like having a camera on a stoplight or an automatic camera rigged to a radar gun hidden in the weeds. It does not exist as a deterrent--a police car would do more, it exists to produce revenue.
Having automatic systems to record your violations, purchased by you at your expense makes the whole idea even more cost-effective. Stiff fines, forced labor ("commmunity service"), etc. all can be levied on the violator, and even more drastic measures on the black marketeer, whose very existence would justify large labor segments of government jobs. Call it something catchy like the "War on Fat"...
I'd be more concerned about private enterprises using the data. Figure before you go to buy health insurance the company runs a scan of shopping habits -- purchased from grocery stores, credit card companies etc. -- to see if you're eating healthy and not taking risks.