I think the connection is insulin and insulin resistance.
This is how I understand it (please correct me if I'm wrong anyone
)For those of us with PCOS, the high insulin levels are one factor that cause our ovaries to malfunction and produce higher amounts of androgens and estrogens, and less progesterone. Thus the acne, unwanted hair, skin blotches, and even hair loss. The high estrogen levels also put us at higher risk for certain cancers, such as ovarian and uterine.
Insulin is also the "fat-storing hormone", and especially contributes to storing fat around our internal organs (the "apple" shape) as well as fat everywhere else. It is practically impossible, short of starvation, to lose weight when your insulin levels are high, and eating lots of carbs are one way to keep your insulin levels up there even when you are low-cal. Low carb, on the other hand, lowers and regulates our insulin levels. We lose weight, become less insulin-resistant, and PCOS symptoms improve.
There is a lot of information on low-carb and weight loss and how it works in the main forums, but you will really need to pick a plan and read the book for that plan to be sure you are getting it right. You might want to see what the other women are doing in this forum to help you choose; I myself like high-fat Atkins and have had excellent results with both weight-loss and PCOS, but people have had good success with other plans too.
best of luck!