I've written a blog post on "Body Mass and Risk from COVID-19 and Influenza", available at https://radfordneal.wordpress.com/2020/04/06/body-mass-and-risk-from-covid-19-and-influenza/
Here's the intro:
Understanding the factors affecting whether someone infected with COVID-19 will become seriously ill is important for treatment of patients, for forecasting and planning, and — with factors that can be changed — for personal decisions aimed at reducing risk. Despite our current focus, influenza also remains a serious disease, so understanding its risk factors is also important.
Here, I’ll look at some of the evidence on how body mass — formalized as Body Mass Index (BMI, weight in kilograms divided by squared height in metres) — influences prognosis for respiratory diseases. Information specific to COVID-19 is still scant, but there is more data on influenza and on other respiratory infections (which includes coronaviruses other than COVID-19). Information on how BMI relates to general mortality should also be helpful.
Below, I’ll look at two relevant papers, plus a preliminary report on COVID-19. To preview my conclusions, it seems that being underweight and being seriously obese are both risk factors for serious respiratory illness. Furthermore, it seems that “underweight” should include the lower part of the “normal weight” category as defined by the WHO. Official advice in this respect seems dangerously misleading.