I have no evidence, just observation. With regard to obesity, it's a relatively newer problem compared to smoking and I haven't seen nearly as much public facing campaigning to fix it. For example, I don't think I've ever seen a PSA about eating less, whereas I've seen literally hundreds about cigarettes since I was a child.

Admittedly, most anti-obesity campaigns also seem to be neutered by lobbying. "Stop drinking soda" becomes politicized and turned into "move" by lobbyists. Taking a 30 minute walk is great advice for overall health, but will do absolutely 0 to address obesity.

I guess overall, there's no guarantee of success here, but I tend to view the shift in public sentiment about tobacco as a direct result of public health efforts. Which leads me to believe it's at least possible for other issues (obesity, alcohol). But certainly it is difficult and with unknown risk of failure.