Healthy weight range depends on your frame size. Here's a portion of the height/weight chart for women:
Height Small Frame Medium Frame Large Frame
5'6" 120-133 130-144 140-159
If you don't know how to tell your frame size, look at your hands/feet; are they considerably smaller/larger than others your height? Are you shoulders narrower/wider?
Your weight also depends on muscle mass. If you're very active and have a lot of muscle, chances are, you will weigh more than someone who doesn't have a lot of muscle.