This is a lie perpetuated by magazines that want you to keep buying.
If you want true, long lasting results, lower your processed simple carbs and start eating micro nutrient rich foods. Vitamins, minerals, proteins, fats, are all ESSENTIAL! Once you have your eating under control, shimmy over to your local store and grab a copy of either Oxygen Magazine, Muscle and Fitness Hers, or Fitness RX for women and learn about lifting. Small weights will not help you get stronger. EVER. You will stop seeing results if you don't challenge your body and that will derail your fitness attempts.
You can do it. You can be one of those women who have tight bodies, even after you have kids.
Ladies I follow for inspiration:
These ladies give you a ton of motivation an you will see what heavy lifting will do. I understand the fear of getting too big, but the amount of work it would actually take to build the amount of muscle necessary to look 'bulky'. It will take yours and nutrient manipulation. It won't just happen from eating right and lifting heavy.
You can do it. You can have that strong, cellulite free body - but you need to eat and work out hard to get it.