Weights necessary????

Weight training significantly helps with weight loss. The more muscle you have the more calories your body burns through the day with less effort.

if you have arms then you don't need weights. Do push ups, reverse push ups (for your triceps), crunches, bicycle crunches, planking. There's a lot you can do with your own weight. But you can pick up a 40lbs set of dumbells at Walmart for $20

My coaches and nutritionists in college always told me to think about it this way: lower body fat percentage is better for your body. We can all agree on that. If you are strength training (with heavy weights) and increasing the amount on muscle you have, but your weight is staying stable or going down, then by default, your body fat percentage is going down. This is what leads to that toned, sculpted look.
After all, who wants to be "skinny fat"? It's not healthy, and doesn't help you look better naked, to be blunt.
A great book to read is "The New Rules of Lifting for Women". It has a lot of great info about why women (and men!) should be lifting weights.

I am a little biased because I weights, but the truth is while weights themselves are not necessary weight training is. Whether the weight is in dumbbell/barbell form or if you simply use your own body is a matter of preference. Weight training burns more calories than just cardio, like dtorres21 said your body needs to repair those micro tears so it will be using calories well after you stop exercising. Cardio only burns calories while you are doing it. It also is beneficial for women to reduce bone density loss, and helps avoid osteoporosis (I really hope I spelled that right, lol). Personally it acts as an appetite suppressant as well, but that isn't a guarantee for everyone.