The U.S.A is by far the largest country with the most overweight people. Although in other countries the percentage of people who have overweight is heigher:

% Overweight
1. Nauru 94.5
2. Micronesia, Federated States of 91.1
3. Cook Islands 90.9
4. Tonga 90.8
5. Niue 81.7
6. Samoa 80.4
7. Palau 78.4
8. Kuwait 74.2
9. United States 74.1
10. Kiribati 73.6

source: http://www.epidemiologic.org/2007/02/most-overweight-countries-in-world.html

The interesting wording of the question has me pursuing a different answer here:

Let's parse it out: "In which part the world ..."
There's no mention of nation-states, and "world" implies the planet, so as a whole. The first part of the answer is overweight people are found on the surface of this planet, at a depth into the oceans at which submarines operate, and to a height in the atmosphere at which modern aircraft function.
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Emekus doesnt mention whether he's including deceased "fat" people ... However that would only have a small effect on the answer if its folded into the aircraft-to- submarine answer segment above. The cremated dead, or those accidentally or purposefully, ceremoniously or homicidally buried-at-sea, now extend the answer to the bottom of the ocean and the lowest extent. If those ashes are scattered to the wind, then the upper altiitude answer would now be to up to whatever level particulate matter can rise to.

As it turns out, particles have been detected as high up as 50,000 feet. See
http://adsabs.harvard.edu/abs/1958AJ.....63..306H
Interestingly some of the dust at that level is distinctly extraterrestrial in origin.
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Finally, "predominantly" means more than half. So the question is where are the people with a Body Mass Index (BMI) value of 51% or higher?

Well, the only solid answer so far is: they are between the bottom of the oceans and 50,000 feet into the atmosphere.

This last sentence may be my complete answer, since my attempts to find worldwide by-nation statistics indicating percentages of BMI plotted against total populations of various countries, has me thinking that this data set has apparently not been systematically and globally collected.

In addition if we were to commission a global survey to acertain the geographic-by-nation-states distribution of people with a BMI of 51% or greater, we are then confronted with the time element. If we take those numbers on a given date and time, worldwide, then one day or minute later, the distribution and numbers have changed, as people move across national boundaries, are born and die.

Thus, a methodology would have to be agreed upon. Me: "How about a monthly world-wide survey for 51%+ BMI individuals as a percent of total national population, and then compiling yearly averages for every nation." Someone else: "okay. sounds good." (That was easy!)

Finally, I would have proposed that we commission a 10-year study to do monthly surveys of the member states of the United Nations. Then, once we have all the stats compiled for a 10-year run, based upon the detection of a trend or trends in the data or even of no trends in the data, we would finally be able to answer the question definitively and also be able to comment on any trends detected over time, which might enable the study to have some applicability to a few future years where me might be able to conclude that the probably future conditions in the relevant areas of the world will have a predictable increase or decrease or remain stagnant and unchanging.

Moral of the story: How you word a question, what information you need to extract, and for what purpose and with what budget, and over what period of time all have critical impacts on your answer, and can radically change the results. -- And statistics are only as valid as the last twist that someone made to the data collection parameters.

Im having some fun here (I think!), but this is my way of emphasizing that the precision with which you ask a question has everything to do with the precise answer you'll get. And reading in our own assumptions to fill in the gaps in a question, is to risk inject our biases into the question as well.

Arjo's answer seems spot-on. Yet let's look closer at Arjo's data. It's dated 2007. So just by that, it is out-of-date. For each country listed, was the data collected using the same criteria? In the US, we do an every-decade national census. In between years ending in 0, our data is based on fractional polling or extrapolations of previous trendlines. Is weight recorded as a data item in the this census? I don't know. Well, then, they must do it by driver's license. but what percent of the populations in each country dont drive and what about pedestrians, how do we measure them? And if we use driver's license data, is it reliable? In states in the US where I've been licensed, the weight number is a number I gave them of the weight I expect to be at by January after my New Years Resolutions get acted on. So this data wouldnt be valid, if it's self-reported and without any scientific verificiation.

How about a data search through everyone's medical records? Well, unless the law has changed, disclosure of information from your medical records is a violation of your privacy rights, unless you sign a waiver releasing that information for the purpose you specify.

Unless someone remembers that they were interviewed by their government about their current weight in 2007, or that you reported your weight to the governemnt that year, then *maybe there was no comprehensive survey done that year.* The epidemiologists are probably making estimates. And would the reliability be inversely proportional to the extent to which the epidemiologists involved were motivated to inflate the figures in order to justify the awarding of a government grant for further study of the issue? But of course.

So, we end with the only verifiable and actual information that we know for a fact: the answer is ..... between the ocean bottoms and 50,000 feet into the atmosphere.

From all the News reports supposely quoting Doctors: The USA...

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