I made the connection myself. We know where the high death rates are in the US, this resource shows that the epicenter in the US (NY area) does not correlate with obesity levels in the US.
NY has 97 deaths per 100K residents, and obesity rate of 25-30%
CA has 3 deaths per 100K residents, the same obesity rate as NY
ND has 2 deaths per 100K residents, obesity rate >35%
IA has 3 deaths per 100K residents, obesity rate > 35%
One would assume that obese people have a compromised immune system(*) - which could lead them to higher death rate - but the issue here is the health and effectiveness of the immune system, and it does not matter if it is compromised because of age, obesity, smoking or genetic reasons.
(*) -
https://www.ncbi.nlm.nih.gov/pubmed/22429824
FWIW - Italy has high death rates, but it is one of the lowest obesity countries in Europe. On the other hand, it has a large elder population - which is why the death rate there was/is so high