Obesity --The World Health Organization has data on the proportion of a country's population aged 20+ that is overweight (BMI>=25) and obese (BMI>=30). The data can be downloaded in spreadsheet format at http://apps.who.int/gho/data/node.main.A896?lang=en . Unfortunately the column which includes the actual data is in text format and includes the average estimate as well as a high and low estimate. The downloadable spreadsheets are made up of several worksheets--the data is found on the "data" worksheet. The same web page makes data available in two tables for mean BMI trends with data from 1980 to 2016. The downloads for these two tables provide data with both all of the data combined in one column, but with the data also provided in numeric format in separate columns.(Both WHO and UNAIDS tend to provide data downloads with three levels of estimates jammed into a single text field. You can find suggestions on separating the data in spreadsheet format in this web site here ).
In a report in PDF format -- "Obesity and the Economics of Prevention:
Fit not Fat" at http://www.oecd.org/els/health-systems/46044572.pdf
the OECD provides data on obesity in its member countries. Individual
country data is available in the "Media Briefs" section of the page
while the link given at "Underlying data and charts for all the graphics
in the media briefs are http://www.oecd.org/health/health-systems/46071157.xls
also available as an XLS file and provide time series data for all the
member countries -- several different series are provided although the
data is messy and would have to be reformatted for use in a database.
Other nutrition pages: