Genetically modified crops were introduced commercially in 1996. Advantages were to include more resistance to pests and less need for herbicides however the pests and weeds have become resistant to the modifications.  We don’t really know the long term effects of the foods on human health.
A disadvantage of the modified corn is that the grain itself was modified to produce internally a chemical harmful to pests. Bt corn produces a protein derived from the bacterium Bacillus thuringiensis. The Bt protein content of pollen from the GM corn was found to be harmful enough to negatively impact the larval stage of Monarch butterflies in areas adjacent to corn fields.  Typically a pesticide is applied to the exterior of a food and is removed before eating by washing or peeling the food. Clearly a modified grain that forms a pesticide within the food itself has disadvantages in that peeling or washing can’t remove the pesticide from the food. So in 1996 an interesting experiment was begun with the food supply and it is still taking place.
The following link is to an animated map which shows the increasing rates of obesity in the US between 1985 and 2010.  The animation is a little fast over the 25 year time span but it can be seen that more categories had to be added during the 1990s when the map changed from mostly pale blue (10-14%), to dark blue (15-19%), and to peach (20-24%), around the year 2000, and then advanced to orange (25-29%) around 2007, and finally red (>30%). The overall rate for 2011-2012 was 34.9%. 
We had sugary foods throughout the 1900’s but we didn’t have Bt corn as 76% of the corn crop  or other genetically modified foods. Not enough is known about autoimmune and fertility risks that may be associated with Bt corn or other genetically modified crops.  Gliadin, one of the types of protein in wheat, may be associated with an autoimmune type of diabetes  as well as the autoimmune condition of Celiac disease.
/Update, 11/3/2017 – the Roundup herbicide which contains glyphosate and which is frequently used with genetically modified crops and some other crops, may also be affecting physiology in a way that increases risk of weight gain and high blood sugar due to inhibition of CYP enzymes. This is still considered hypothetical rather than proven information however – more research is needed.
/Disclaimer: Opinions are my own and the information is provided for educational purposes within the guidelines of fair use. While I am a Registered Dietitian this information is not intended to provide individual health guidance. Please see a health professional for individual health care purposes./