Re: how much should a 5'3" 50 year old woman weigh
The usually given range based on BMI of 19 to 25 is 107 to 141 pounds for a 5'3" adult.
However, be aware that body fat percentage is probably more relevant for health. You can be within the range given above, but be unhealthy due to having too much body fat. Conversely, you can be heavier than that range, but if the extra weight is muscle, you will not be at the added risk of problems due to excess body fat.
A commonly used proxy for body fat is waist circumference measured at navel level. A typical goal for good health is to get it to no more than half your height and no more than 0.8 times your hip circumference (for women; 0.95 times hip for men).
Note that it is common for those beginning an exercise program to gain muscle, which may mask decreases in body fat if one looks only at the weight scale. If you want to track progress, you may want to track body fat percentage and/or waist size as well as weight.