I haven't tried Zumba but my guess is, as with a lot of the "dance" type classes and videos that although they are fun and get you moving that they probably do not get your heart rate up too high and might not be the best form of cardio for weight loss. But I could be wrong since I've never tried it!
Some advice from someone who's been there done that (I lost 50 lbs after my first was born). Be patient, 15-20 pounds in 6 weeks is a lot. Aim for about 1.5-2 lbs a week if you really want to keep it off. I would do some form of weigh lifting 2-3x a week and then some form of cardio 2-3x a week. P90x are good and includes both weight lifting and cardio dvds (see if you have a friend you can borrow them from, I feel like there are a ton of people with the dvds just sitting around their house). A brisk walk with something like jumping jacks or some other power move every five min or so to get your heart rate high would work well for cardio. If you can't join a gym for weights get some resistance bands or buy some hand weights.
But most of all remember its 80% what you eat and 20% how much you work out. If you can't afford weight watchers, you could try counting calories, there are a TON of free programs on line to help you figure out calories and track them, sparkpeople.com is good as is myfitnesspal.com
I use a personal training type website called phit-n-phat.ning.com where I get a lot of support and download workouts and such. Its been helpful for me and its relatively cheap.
Good luck in your journey! If you do try zumba give us a report! :)