you specifically mentioned, since "refinement" of sugar and carbs. As a recent development, dishes even peasant dishes contained pasta's, oats, rye, and barley, wheat was "upper class", sugar and honey was also used since the medieval times, considering even the poor had access to things like honey and sugar, obesity has been going on quite a long time even before the industrial age, or refined, it isn't some thing that is well documented, it's not like you can tell the skeletal difference between a obese and thin person either.Your implying that obesity is a recent development with the original statement you made. Which it is not.
Obesity can be traced back at least 12 000 years, with increased food security, being an example.Venus of Willendorf fertility doll some speculate as indication of obesity being present in societies already, 22 000 years ago.
Food securirty and population growth, and life expectancy and documentation just made it more pronounced.Thousands or 100's of years ago the world population was significantly smaller, a 1000 obese people in today's terms wouldn't be out of the normal, it might have been back then.
Also have to consider you don't get fat just from sugars and carbs, any rich food source that is secure and plentiful will do that.It has been shown once food security is in place, societal importance of gathering or hunting food drastically shifted over time.In other words people became lazy gits........