Weight lifting in the context of strength training (also called resistance training) is an important part of an overall fitness program regardless of age. In fact, research shows that even people in their 90s can improve their strength and walking speed through weight training.
I discussed your question about "heavy" weight lifting with fitness expert, Dan Bornstein. He explained that he defines "heavy" as enough weight to prevent an individual from completing eight repetitions of an exercise because of muscle fatigue or failure. For example, if you were working with a 10-pound weight and could not successfully repeat a move eight times, the 10-pound weight would be too heavy for you. Ideally, to build strength, you should be able to do two or three sets of eight to 12 repetitions with good form before the muscle that you are working tires and "fails." Once you can do three sets of eight easily with perfect form, you generally can handle a bit more weight.
If you're new to strength training, I urge you to work with a trainer or coach if possible. They will help you learn proper form in order to avoid injury and to perform the exercises properly for the effect you want. Look for a trainer certified by the American College of Sports Medicine or the National Strength and Conditioning Association. If you can't afford a trainer, you can learn strength training exercises from the many books on the subject. One that I recommend is "The Whartons' Strength Book" by Jim and Phil Wharton and Bev Browning (Times Books, 1999). Dan Bornstein makes the point that as long as you learn correct form, age has little to do with the amount of weight you should be able to lift in a program aimed at building muscle and increasing your strength.
I applaud your interest in strength training. It can help prevent osteoporosis, maintain mobility and prevent falls and is equally important for men and women.
Andrew Weil, M.D.