Ummmm. That's just not true though is it. Most of the third world lives off carbs, and they are generally not obese.
A few points:
Actually swelling in the stomach and often limbs are associated with poor diets in the majority world. Various conditions of poverty and malnutrition feature them. Remember the round bellies and thin limbs on TV? Doing famines in China, oedema was a massive issue.
Third World is an outdated and very silly term. I mean who refers to the Second World any more?
By the time people in the majority world get underweight it is very very bad, associated with a drop in IQ, lifelong health issues, including things like resistance to disease and cardiac problems. Having so few calories that you are properly underweight on carbs is quite difficult.
Obesity is an issue in many majority world countries as well. Not to the same extent as the West but certainly when people have the opportunity to gain weight, they do. In epidemic numbers, depending on the country. In Libya Egypt and South Africa, the obesity rate is around a third of the population.
The issue often is the media likes to ,show big people at the foodbanks and skinny Africans. For the same reason, bias.