Because obesity makes it more likely you'll end up taking up a hospital bed that someone else might need.

Obesity isn't contagious, so it doesn't really tax healthcare systems like a virus that produces exponentially increasing demands on local healthcare systems.

It's kind of like trying to compare O(n) to O(2^n) without admitting that [the system was operating fine in the O(n) regime and is falling apart in the O(2^n) regime]. My sister-in-law is a nurse practitioner and she has been reposting job listings for RNs and NPs over the past year or so offering $6k+ per week (!!!) for RNs and NPs to do stints in hospital systems under extreme load around the country.

The healthcare system manages this inconsequentially because relative to refusing a vaccine, the increased likelihood of this happening with obesity is marginal.

Prior to the pandemic (and also today during the pandemic), there wasn't a concern about people dying from treatable medical conditions because healthcare capacity was taken up by those suffering from obesity.