I have been looking for hours trying to find this number, and can't seem to get a straight answer. I've seen some studies that calculate the change in BMI, but for some reason they don't give you the actual numbers, just the rate of change. I've also found information for individual countries, but I want the global average, and would prefer not to do a calculation with 196 different sets of data.
The answer might be a little late, but it was published after you asked the question. See the following publication for estimated global BMI averages from 1975 to 2014: http://thelancet.com/journals/lancet/article/PIIS0140-6736(16)30054-X/abstract
World Health Organization data
World Health Organization (WHO) is your friend for this kind of question. You can find loads of data on BMI per country, per region, per sex and even see the individual data points on here on the WHO website. They also have maps and graphs. Have a look!
Graphics from daily.co.uk
Daily.co.ok have an article (there) with some interesting graphics that I am reporting below. Please note that they made a mistake in the header of each graphics, so just look at the bars below the map and not the range indicated above the map.
Here are some countries with...
...the highest BMI:
... average BMI:
... low BMI:
... the lowest BMI:
You might also want to play around with this applet on the BBC website who allows you to compare yourself with the average in your country for your gender and age and the world wide average for your gender and age. For example, I entered my personal data and it allows me to see that 69% of the world-wide (my age category and gender) population has a lower BMI than me and 64% of the population of the country I am living in (my age category and gender) has a higher BMI than me. This number goes down to 56% when considering the country where I grew up.
I don't think that knowing the world average will tell you much. What is important is to consider variation within countries, comparison between countries and consider age category and gender. The WHO data set indicate the percentage of individuals that is in a given BMI range per country but not the average value from I got so far.