Obesity isn't the main factor, as far as why Italy infection rate & mortality is so high.
They've been saying from the start, that Italy has an older population that the US... especially in the infected regions. They also still enjoy having those large weekend family gatherings (like I remember as a kid)... that aren't as prevalent in the US anymore. Toss in the double tap cheek kissing, & the fact that in Jan a lot of Chinese from Wuhan flew into Italy... (Chinese have a lot of fashion operations in Italy... they want to use a "Made in Italy" label) It's little wonder that it spread quickly, as people there went about there normal routine for weeks, before they even realized it was in the country. With the exception of the large cities, the US has a lot more wide open spaces, with more of the population living further apart. I can't even see my neighbors, & I'm less than 3miles from the edge of a city.

Of course I still think some of it spread via the mail here in the US.
When it 1st hit our State... it slowly started spreading outwards from Phila & Pittsburgh
But jumped to Harrisburg, right in the middle of the State within just a few days.
Why Harrisburg....
Because a few years ago they decided to hub nearly all of the States mail into Harrisburg every night.
If I mail a letter to my neighbor,,,
It goes from my box to the York PO, then to Harrisburg PO, then back to York PO & finally into my neighbors mailbox.
They no longer separate out local mail at local PO. (Except a few small ones that will still do it if you drop it off at their office)
FedEx & "UPS also have big operations in Harrisburg, next to the Airport..