I do not believe you being underweight is a cause. There may be a correlation between your acne, weight loss and something else. But correlation =/= causation. I've seen overweight people with plenty of acne and tiny people with flawless skin.
Acne has more to do with irregular blood sugar control and inflammation. Of course, the causative factors in individual A might not be the same in individuals B and C. In other cases toxicity, stress and hormonal imbalances have a role. You will have to do some trial and error to figure it out.
Look into your digestion. Poor digestion has been linked to it. Acid reflux and the like tend to exacerbate the situation. A friend of mine had a bad case of bacne (back acne), and she linked it to malabsorption. But again, it might not be the same for you.
Also ... eating the 'right foods' can be tricky. If blood sugar issues and inflammation are at the heart of your problem then you might want to avoid (or cut down) starches and other foods that may affect blood sugar stability. Sugar is your enemy if you suffer from acne.
Also ... the colon is the primary place you have to keep in check for clear skin, and that includes acne. Keep you colon healthy and it will help promote better skin.
Give me an example of your typical diet (throughout the day). Do you consume wheat products? How much water do you drink daily? How often do you eat?
You'll need to do trial and error to figure it out. Variation and selection is the best process, and it may take you some time, but the end result does justify the means in this case.
I'll be happy to share with you what I know if you need any assistance.
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