"Obesity costs the US healthcare system almost $173 billion a year."
So that's about 6% of the difference? I'm not immediately saying no, but it sounds like that's not the real problem.
Social reasons it would never work. I hate to mention anything race related online but simple truth is America has complicated history and African Americans are 30% more likely to be obese than White Americans and also earn approximately 60% of income that whites earn. A fat tax, especially one that properly allocated the cost burden to the individual, would erode race relations.
Fat shaming! ... It makes me sad whenever I hear that response to any mention of the health problems associated to obesity.
That 6% number isn't even close to accurate. There are many other very expensive chronic conditions that are downstream of obesity including type-2 diabetes, heart failure, hypertension, MSK injuries, etc. We are digging our graves with our teeth.