Weight training, especially for those over 50 years, is recommended by the American College of Sports Medicine. Looking like a body builder with bulging muscles is not what you should be after; rather, using weights to help prevent muscle lost and enhance movement, especially in arthritic joints, should be your goal.
As always, consult a doctor before you embark on a new exercise, like weight training. But once cleared, incorporate weight training at least two consecutive days a week into your exercise program.
Develop a routine to workout all muscle groups. It may prove beneficial to go on-line and search for the program that best suits your needs; or, you can ask someone at a health club, recreation center, or senior center, that is most familiar with weight training to help you design a program.
Start out with light weights and strive to do each exercise, once, 10 to 15 times. If 10-15 times is too easy then increase the amount of weight. Make sure you use the proper form for each exercise to get the maximum benefit out of it. Also make sure you warm up before attempting to lift heavy weights.