My gf is 1.55 m (5'1") tall and weights 40 kg (88 lbs).
Considering everything else to be at normal parameters, is it healthy to be really this tiny?
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There are health risks associated with being underweight. The NIH BMI calculator returns 16.6 for a 5'1" 88 lb person and says anything under 18.5 is underweight. There is less information available about the risks of a low BMI than a high one, but I found a page from the NHS in the UK. It suggests fatigue and a lowered immune system are worries.
There is a difference between being very thin even though you eat and move normally, and being very thin because you are restricting your diet. There are also health risks with losing weight quickly. All of these are things for your friend to discuss with her own doctor. A single point like a height and a weight is useful to confirm "yes, that's a really thin person" but not for anything more such as "you should stop dieting" or "you should try to gain weight."