Your basal metabolic rate is the amount of calories your body burns every day at rest without you doing anything. It is largely dependent on age, gender and genetics.
As we get older your BMR unfortunately slows down making it easier to gain fat as we age. There are probably many reasons for this but one main reason could be a loss of muscle tissue.
Muscle is not a massive calorie burner. To maintain 1 ib of muscle seems to require around 10 calories a day. To build a pound of muscle requires lifting heavy weights and is not a fast process, especially for women due largely to a difference in testosterone.
So I feel the real value for performing weight training in terms of increasing metabolic rate is to be able to maintain muscle tissue rather than losing it.
Use it or lose it!