What is a healthy weight for me?

All the websites, at most, use BMI which do not take into account bone structure and muscle mass so the weight they state are not accurate and should be used as a guideline. However, at 113, you seem a bit light for your height, 120 all the way up to the suggested weight that the websites told you, 132, seem like a healthy weight for you. As most females are, you’re probably just more focused on getting the socially accepted, attractive flat stomach, thigh gap, completely flab-less etc, and therefore you felt the need to lose weight at 120. 120 is perfectly fine at your height though there is nothing wrong with eating healthy and exercising. Just focus on eating healthy (which also means a good amount for you), you don’t need to lose weight AT ALL especially with the weight you lost already, and you will be fine.