hi and welcome. My guess is, after years of believing the low-fat myth (a must read on this topic of fat intake and health is the Taubes Science article--available at
http://ajdubre.tripod.com/Health/So...ietaryFat0.html ), you probably aren't eating too much fat. I bet you haven't yet stuck a spoon into a stick of butter or vat of cream cheese or cooked up a whole pound of bacon as a snack.
Yes, if you ate far more in calories as fat than you were expending as energy, you wouldn't lose weight. But in the absence of high levels of insulin, you wouldn't store it, either. It'd come out as waste (and you might get diarrhea as a result). You might want to utilize
www.fitday.com to make sure your calorie intake is right at 11 or 12 x your body weight in pounds (or about 1550-1700 calories for you). For the "average" person, this, LC, all whole fresh foods, no sugar substitutes, limited dairy, and some moderate exercise would provide the optimum weight loss conditions. With so little to lose, once you've gotten your induction results (typically 3 or so pounds for more slender people), you'll probably only lose at .5-1.0 pounds per week, on average.
All that said, you could be different. Your metabolism could require more calories (eating fewer than 1400 would likely send you into "starvation mode" and your body would refuse to give up any fat molecules at all), 50 g of carbs instead of 20 for optimal loss, no dairy at all, caffeine might help you rather than hinder you, or so on. The only way to know is to pick the plan, stick with it, and be satisfied with anything around a half pound loss per week. If you don't lose pounds or inches for three or four weeks, then it may be time to start experimenting a little to see if a dietary or exercise change could get the fat moving again.
Hope that helps!