The BMI-based "healthy weight range" corresponding to BMI of 19 to 25 is 104 to 137 pounds for your 5'2" height.
However, while going by weight alone may work for population studies, individuals can vary considerably in amount of body fat. A muscular athlete may be "overweight" (BMI > 25), but not be overfat, and therefore not at increased health risks associated with being fat. Similarly, a fashion model may have a low BMI, but have a high body fat percentage due to having little muscle, and therefore have increased health risks associated with being fat.
You may wish to frame your goals and progress tracking in terms of body fat percentage rather than body weight. Or at least some proxy like waist size (for women, less than half your height and less than 0.8 times your hip are typical goals for good health).
Any ideas?