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.
The campaigns against obesity don't make people thin, because half the time they don't even promote stuff that makes people thin. Half the time they promote diets that makes situation worse in the long term.
Campaigns against smoking did worked in the past. Drug use is down. Teenage v pregnancies are down. All stuff that involved campaigns.