In the cited article, the only statistic I see on weight specifically is that 74% of critically ill UK patients were overweight or obese, which makes it a risk factor but not the be all and end all, given what fraction of the whole pop fits that category (~65%).

It also says that 99% of deaths in Italy were from patients with pre-existing conditions, which would included weight related and non-weight related ones.

Regardless of COVID, maintaining a healthy weight is probably one of more important lifestyle changes one can make to reduce risk of overall mortality.