One of the consequences of a sedentary lifestyle, dieting, and aging is a drop in lean body mass. With the drop in lean body mass there is a drop in resting metabolism and daily caloric expenditure.
This means you require fewer calories (and less food) to maintain your body at its present weight.
While weight lifting itself doesn't burn a significant amount of calories, the benefit of added or maintained muscle mass is significant.
Often with diet alone, fifty percent of the weight loss is from lean tissue. When diet is combined with resistance exercise there is an insignificant loss in lean tissue - weight loss almost exclusively coming from fat.
In fact, often there is a gain in lean tissue and a slight increase in resting metabolic rate (more calories burned per day). A gain of 4.5 lb of muscle mass is estimated to increase resting metabolic rate by about 50 kcal per day.
Besides the obvious gains in strength that result from weight lifting, perhaps one of the most meaningful benefits of weight training is its ability to help prevent loss of muscle mass that naturally results from dieting, aging, or inactivity.