Weight is determined by muscle mass, and your body frame. As you know muscle weighs more than fat therefore you can look leaner and be healthy yet weigh more than someone who looks fat and is unhealthy.
Your body frame can also play a factor into your weight. A quick way to determine your body frame is to wrap your middle finger and thumb around your wrist. If your fingers overlap then you have a small frame, if they just meet then you have a medium frame and if they don't meet then you have a big frame.
With this in mind, a healthy weight for a height of 5'1 is between 108-129. To get a more accurate answer catering to your body frame visit this website http://www.healthatoz.com/healthatoz/Atoz/tl/cl/healthyweight/healthyweight.jsp?h=0&frm=0