Have a feeling that this is going to turn out just like how it did the last time I decided to open up this particular can of worms on this site, but hey, I'm not afraid of the interwebz vegan police...I just hate seeing people make such radical alterations to their diet for the sole purpose of shedding pounds.
You DO NOT have to go vegan in order to lose significant weight. HOWEVER, if you have an honest interest in the vegan diet/lifestyle, then why not go for it. You only live once.
Weight loss is a result of burning more Calories than you consume on a regular basis, over a period of time. Well, that's the short answer. You can have 1,200-whatever Calories of junk every day (I feel like 1,200 is standard for weight loss, but you'll need to talk to a doc about that) and feel like a lethargic bag of s!@# all the time. Or, you can have 1,200 Calories of high-energy carbs, lean proteins, fruits, and veggies, and feel even better than you did prior to starting your diet. Both methods should result in weight loss, but you'd also need to tailor your healthy diet (...you'd go with diet #2, right? Right? Haha) to your own needs. Factor in how much exercise you typically get per day, your health conditions, etc.
So you have PCOS? I'm not a doctor -- just an individual who enjoys studying health and wellness -- but I've heard that some people use diets high in soy to combat PCOS. Soy contains estrogen, and hey, it's also vegan -- yay?
And, lastbutnotleast, a fun fact. This kinda relates to my first point, and it's also for anyone on here who's previously referred to me or another omnivore as an overweight, unethical slob, etc (seriously, it got really nasty last time) --
I'm an omnivore with a plant-based diet. Lean meat is a 3-4x a week thing, while low-fat dairy is an every day thing (mm, yogurt). Fruits, veggies, and grains are all-the-time things.
I'm pretty active. I can kill a mile in about seven minutes and barely break a sweat. Can run 3-5 miles on flat terrain before getting worn out. I can do between seven and 10 pull-ups on a good day, and can pretty much hoop until the cows come home.
I eat between 1,500 and 2,000 Calories a day, and -- gasp -- have brought my BMI up to 19.5 (normal) from 18 (underweight) for the first time EVER, this year. The body mass index isn't always the best method of analyzing someone's weight, but I don't have a ridiculous amount of muscle, so it serves just fine here.