This study published in late May 2020 contradicts earlier research and concludes that weight is not an independent variable for COVID-19 severity. The study, like all research, has its limitations. For one thing many study participants did not have an outcome (either recovery or death) by the time of the study cutoff. But it’s a clear picture of severity of the corona virus being dependent on multiple pre-existing conditions. According to the authors:

We identified older age, cardiopulmonary comorbidities, and higher concentrations of D-dimer as independent risk factors for poor outcomes. Higher concentrations of IL-6, which have been observed among patients with COVID-19 with more severe clinical illness were also associated with in-hospital mortality.

Consistent with other studies this one found that two-thirds of those with severe symptoms were male, the median age was 62, and 82% had at least one other chronic illness. But, this study did not find that weight, even BMI above 40, was a risk factor independently of other conditions.

You can find the full text of the research at the link below.

Epidemiology, clinical course, and outcomes of critically ill adults with COVID-19 in New York City | The Lancet