Weightlifting. Lifting weights is the classic strength-building exercise. From triceps kickbacks with 5-pound dumbbells to Olympic lifts with 500 pounds on a barbell, anyone can do weight training. And it's not just dumbbells and barbells; you can use machines, resistance bands, kettlebells, medicine balls and many other pieces of equipment. Weightlifting also often includes accessory exercises using body weight only.
Many of the activities you do to build strength will also help your balance. Balance is partly a matter of developing your small stabilizer muscles that provide support and keep you steady. Free weight exercises, such as lunges and deadlifts, will help strengthen the stabilizer muscles. Even better, include some single-leg exercises, such as single-leg deadlifts and pistol squats, in your strength-training routine.