You want it to be fun, bearable, and gratifying. If the weights help with this, use them, by all means. If they have the opposite effect, don t use them. Think enjoyable, think long-term. While it is true that muscle weighs somewhat more than the fat it replaces, the effect is very small in most cases.
Muscle is good, so never shy away from something that helps build muscle.
You might consider reading a good book on physical activity. It would answer this question and many, many more, including how to stay motivated and how to make it fun. A superb book on increasing physical activity is Active Living Every Day. It is by Dr. Steven Blair and colleagues, the world s leading figures on activity. I hope this helps.