Interestingly, the whole thing now seems to have turned into the opposite. sugar = bad, fat = good. But that is not true. Sugar is actually only problematic because it's a bit addictive and it's easy to eat a lot of it. The real problem is taking in too many calories (in whatever form) and/or burning too few.
Carbs cause a sugar rush and after the pancreas deals with it, you get hungry again a couple of hours later. This is why people snack between meals, increasing their caloric intake. If you avoid carbs and focus on proteins and healthy fats, you can go 4, 6 or even 8 hours without getting hungry, effectively reducing your caloric intake.
As a millennial, I remember my Mom buying those Snack well cookies for herself, thinking they were more healthy than traditional cookies. I assume they compensated for less fat with added sugar.