It definitely is a worldwide problem.
Obesity is a major problem in North America, South America, Europe, Australian and Oceania. It's a major problem in the Gulf states too. That leaves parts of Africa as the exception. Perhaps most importantly, obesity is increasing essentially everywhere around the globe and decreasing nowhere as far a I know.
So if we were to select a random person, chances are better that this person needs less food rather than more.
Just saying: obesity can be increasing everywhere, while probability of a randomly selected person needing more food is simultaneously increasing.
Sure, mathematically that is possible (for a limited duration of time)--and it's also possible that more are getting obese while the probability of a randomly selected needing more food is decreasing. Importantly the hypothetical that you describe isn't what is happening. Overall the long-term trend is obviously obesity increasing and hunger decreasing.
"When the rich catch a cold, the poor die of pneumonia."
I'm not sure the obesity problem is worldwide.