Howdy,
So glad you brought the stability ball and free weights. Forget the gym. You are all set, my friend.
You can head over to
http://strength-training-woman.com/s...exercises.html and look at loads of exercises. And guess what... they all include free weights and a ball. And you can do every single exercise at home
In additition to that... here are my 5 tips to fat loss

Enjoy!
1) Eat 5-6 small meals throughout the day. Each meal should be 2-3 hours apart. Each meal should contain one protein and one carb. The first meal should be eaten within an hour after waking.
2) Drink lots of water
3) Rest properly. This means taking at least 24-48 hours between strength training the same muscles, and it also means getting at least 7-8 hours of sleep per night. Lastly, it means taking 1-2 days off from exercising per week.
4) Cardio. This should be done at different intensity levels and different session lengths. Consider doing a low intensity/long session, a high intensity/short session and a few medium intensity/medium length sessions.
5) Strength Training. Strength train each muscle 1-3 times per week. You should lift a proper weight and perform the proper amount of sets/reps for your strength training method.
All of the above things combined will result in fat loss.