Weight training is important for a couple of reasons. First, the more muscle you have, the higher your base metabolism will be and the more calories you will burn even at rest.
But the actual numbers involved in a whole day of "extra" calorie burning due to extra muscle are relatively small compared to the number of calories you can burn during an hour of cardio exercise.
The second reason is more important. Whenever you lose weight, you will lose some muscle along with the fat. If you don't exercise and do some strength training, up to 30% of the weight you lose can come from muscle loss, and that isn't likely to be healthy over the long haul. Good strength and muscle tone are essential for functional living and health. You can hold your muscle loss down to 3-5% of total weight loss with moderate strength training.
Likewise, strength training helps to preserve bone density, balance, and many other important things. So, strength train each muscle group at least twice a week--this really only takes about 30-45 minutes per workout.
Better yet, try circuit training, where you lift weights without resting between sets. This method meets both cardio and strength requirements because you keep your heart rate elevated throughout your workout, increasing the amount of calories you burn per workout.
After you've met your 2 strength sessions per week, focus on cardio if your goal is weight loss. You need the cardio for the calorie burning, and also to build and maintain your cardiovascular fitness.