A small study conducted by researchers at Arizona State University found that low blood levels of vitamin C were associated with decreased fat oxidation - the burning of fat for fuel.
"Free-living individuals with marginal vitamin C status oxidized 25% less fat per kg body weight during a 60-minute treadmill walk as compared to individuals with adequate vitamin C status."
They site a possible mechanism: Vitamin C is used by the body to make carnitine, and carnitine is necessary for fat oxidation.
They also found that the less fat participants oxidized, the greater their fatigue, leading them to speculate that:
"Vitamin C depletion may result in weight gain by two mechanisms: indirectly by fatigability and exercise intolerance and directly by lipid accumulation."
When researchers supplemented the depleted subjects with 500 mg/day of vitamin C, they increased their amount of fat used for energy by a factor of 4.
For the study, published in Nutrition and Metabolism:
Marginal vitamin C status is associated with reduced fat oxidation during submaximal exercise in young adults