I doubt I'd recommend replacing fat with carbohydrates, but you're correct in that sugars (starches/carbohydrates break down into...) cause the body to store fat (more specifically, the elevated insulin levels that accompany this).

Regarding weight loss: I work & exercise with a variety of body types (these body types have people names too!), and, within this small sample, I've found that the dominating factor in overall weight is diet, not exercise.

Essentially, exercise controls muscle tone and how "tight" the skin is, while diet seems to control the overall body shape.