DISCLAIMER: The following discussion only applies to healthy populations and excludes any conditions that may be affected by sugar intake, such as diabetes. I am neither a medical doctor nor registered dietitian and will not be discussing said populations.
Does sugar intake correlate with obesity?
Sugary foods are typically devoid of micronutrients and fiber and have very little affect on satiety (feeling full). This is what we would typically call "empty Calories". That said, it would make sense that sugar would be a primary cause in the obesity epidemic and the two correlate very well until 1999. At that time, sugar consumption began to decrease dramatically; however, obesity rates continued to steadily rise.
So sugar is innocent then? Well, yes and no. Sugary foods tend to be hyperpalatable. This means that they are extremely tasty and also not very filling. This typically leads to overconsumption, thus excess Calories. It's the "You can't eat just one chip" effect.
This is why the sugar source is important here. If you were to have a 12 fl oz soft drink, which is around 40 carbs (160 Calories), where all 40 of those carbs are sugar, this would typically be considered bad. The reason why this is bad is because most people aren't going to say, "Okay, I had this drink which is 40 carbs. I need to eat 40 less carbs in my meal." Most people are going to have the same meal they would have with the addition of the extra Calories from their soft drink. This is also assuming they don't get refills. I've seen people drink 5 soft drinks during 1 meal. That's 800 extra Calories per sitting!
Let's look at a different situation. Let's say you eat 276g (2.25 cups) of raspberries for the same 160 Calories, 33 carbs, and a total of 11g of sugar. For the same 160 Calories as the soft drink, you could have this very filling snack. (You may have noticed I equated Calories instead of sugar. I'll address that momentarily.)
Can you lose weight with a high sugar intake?
We've already determined that sugar intake and obesity rates aren't actually correlated. If sugar isn't the primary cause of obesity, can you lose fat on a high sugar diet? Let's investigate. One study compared two groups. Both groups' diets consisted of 1100 Calories broken down into approximately 11% fat, 19% protein, and 71% carbohydrate. One group had 4% of their total intake as sucrose. The other had 43% of their intake as sugar. The study found similar weight loss in both groups. "Results showed that a high sucrose content in a hypoenergetic, low-fat diet did not adversely affect weight loss, metabolism, plasma lipids, or emotional affect."  Several studies showed the same conclusion. High sugar diets do not impede fat loss.  This is because Calorie intake is the primary determinant of fat loss, gain, or maintenance, not sugar.
Should you limit sugar intake for general health?
Even though sugar intake isn't what is making us fat, it can't be healthy for us, right? Excessive sugar intake certainly isn't good for us; however, when Calories are controlled, it is difficult to eat excessive amounts of sugar. High fiber foods tend to be lower in sugar. That's where our raspberry vs soft drink example comes into play. 160 Calories of a soft drink is 40g sugar. 160 Calories of raspberries, a high fiber food, is 11g of sugar. Another example could be broccoli. 160 Calories of broccoli is 10g fiber and 7.5g of sugar. All that said, if Calories and fiber are controlled, a higher sugar diet doesn't seem to pose any health risk to healthy populations 
Thanks for reading! If you made it this far, I have a special offer for you. I still have a few online training spots left. If you mention during our phone consultation that you read this article, I will give you 20% off your first month!
As always, God bless you AND your family and I will see you next time!