From the article

Sources familiar with SAGE’s work stressed to BuzzFeed News that there was currently not sufficient evidence to prove that obesity itself resulted in increased mortality, and that more research needed to be done. They said that severely obese people are often likely to have other co-morbidities that could be responsible for any worse symptoms.

Older people, men, black and Asian people, and those from socially deprived backgrounds were also seeing worse outcomes, the ICNARC data showed.

It appears other factors are also in play in the UK. Looking at race helps target prevention efforts

Ross Warwick, a research economist at IFS and co-author of the report said: “When you account for the fact that most minority groups are relatively young overall, the number of deaths looks disproportionate in most ethnic minority groups. There is unlikely to be a single explanation here and different factors may be more important for different groups. For instance, while black Africans are particularly likely to be employed in key worker roles which might put them at risk, older Bangladeshis appear vulnerable on the basis of underlying health conditions.”

Accounting for differences in age, sex and geography, the IFS found deaths of British black Africans background to be 3.5 times those of the white British population and British Pakistani deaths to be 2.7 times as high.

https://www.theguardian.com/world/2020/may/01/british-bame-covid-19-death-rate-more-than-twice-that-of-whites

More on obesity from UK

https://www.thetimes.co.uk/edition/news/coronavirus-obesity-doubles-risk...