Lower productivity is an economic issue. It affects employers and the businesses they work in. If they're fired/not hired, then they're dragging us via welfare payments. You are correct on government interdependence wrt Medicare/Medicade etc. However, those programs aren't going away and with around 200 million Americans overweight (and about 70 million obese), their effect is massive.
I don't buy that being fat/obese necessarily makes one unproductive nor severely hinders one's ability to find worthwhile work. A vast majority of the jobs available in America are non-labor jobs (service, medical, and administration); very few of these jobs require one to maintain a healthy weight in order to succeed and be productive. On that note; I'm thinking you meant unemployment benefits when you said "welfare", because one does not receive "welfare" simply for being unemployed. Unemployment benefits have finite time tables (barring extensions) in which the beneficiary must find work, which I've demonstrated above is accessible to the fat/obese. There is the food stamp issue, but I think this is easily fixed by banning the purchase of unhealthy food with food stamps - something I think a lot of people could agree with.
You're absolutely right about Medicaid/Medicare; the fault for this is in the nature of Medicaid/Medicare. These programs need reformed in ways far beyond "the fat person problem". I would like to see more requirements to qualify for Medicaid/Medicare, but that's for another thread.
Define "tackle". I'm all for public outreach campaigns and disincentives for unhealthy lifestyles, but to directly punish the producers of unhealthy food because portions of the population can not control their eating habits seems to be a step in the wrong direction. It is not Company X's fault when rotund teenagers drink an entire 12 pack of their soda a day. This is something to keep in mind when dealing with this issue.
You are correct about the relationship between government and big industry, but that is mostly demonstrative of the failures of asking the federal government to determine which businesses are worthy of subsidies and which aren't - it's the "picking winners and losers" argument. In this context, it's still seems absurd to punish businesses and consumers for poor public policy. Granted, these business
are complicit. Certainly, these businesses could just turn down the subsidies...but that is a utopian demand. No intelligent, successful business person is going to turn down a handout from Uncle Sam on the basis of some half-baked political principle.
As for the tax; I think that, like any sort of junk food ban, is to pass the consequences of individual choices onto businesses and the public at large, including those who practice responsible eating. Furthermore, taxing unhealthy things has never decreased demand or consumption - just ask big tobacco. Tobacco usage has decreased because of public awareness and public service campaigns targeted to the youth. The exploding price of cigarettes has been inconsequential.
This is not to say that there aren't things we can do to disincentive obesity:
1) Public Service campaign focused on the consequences of being overweight: both the economic and health hazards posed by overeating. The message needs to be that it's not okay and that it's unacceptable. We treated smokers with disdain - we said they smelled bad and that we didn't want to be around them and neither should you. Of course that's not what I'm saying about fat people; but the message needs to be as firm as what we did with tobacco.
2) Use tax incentives to encourage businesses to produce food that meets certain health standards. In coordination with an end to subsidies - this could be effective.