For the purposes of this question I want to focus on serious daily sugar consumption. For that reason, I'm only interested in the consumption of semi refined sugars like honey and date syrup in those times, places and social classes where people consumed those things in large quantities regularly (as opposed to just at special celebrations). Has an increase in sugar consumption around the invention and spread of things like refined sugar or increased production of honey, dates etc been historically linked to changes in health measures like life expectancy, infant mortality etc? How do these changes compare to the introduction of other unhealthy products, like the introduction of tabacco to Europe or the popularization of opium for instance?
I would suggest you to read the book sweetness and power by Sidney Mintz. It practically covers the entire question that you are looking for.
He looks at the transition of sugar (refined sugar) as a once elite dish, confection, or work of art to a common staple. Fundamentally, he notes that the growth of sugar gave rise to a tea-drinking culture in Britain during the industrial revolution. Since refined sugar is rich in calories, it enabled the new workers of the industrial age to be fed, with a simple staple of toast and sweetened sugar. With the development of Caribbean sugar, the British diet began to change; previously fruits were not eaten in large quantities due to the fear of diarrhea and other intestinal maladies associated with fresh fruit. However, with the increase of sugar in the market, jams and marmalades began to make headway, and the public's perception of these foods changed.
Alas, I am not an expert in this field, but I think it would be a good starting point.
Mintz, Sidney W. italics Sweetness and Power; The Place of Sugar in Modern History italics (New York; Penguin Books, 1992)