That's true and I agree, but if you're asking why people are dying, you're going to be most interested in the root cause (which should be the variable that is least dependent on the others).

While obesity likely does reduce income somewhat (due to stereotypes), income can be considered an independent variable here.

Relatedly, we know that obesity is very hard to treat, while poverty is incredibly easy to treat on an individual level. The only reason we don't is because people see treatment of poverty as unfair, while treatment of obesity is not seen that way.

I would never claim that income/poverty is the root cause of obesity, as obesity poorly correlated with income in the US.

Obesity is prevalent in both the middle class and poor, with the middle class slightly leading the poor[1]

>39% of people ≤130% of the federal poverty line (FPL) are obese.

>40.8% of people 130 to 350% of the FPL are obese.

While individuals should be brought out of poverty for other reasons, it is not a cure-all for obesity. If anything can be implied by the correlation, it will make the problem worse, and the healthcare system should prepare for this.

[1] https://www.cdc.gov/mmwr/volumes/66/wr/mm6650a1.htm