Initially I had put a single color gradient, but I updated the graph because high density areas weren't standing out enough relatively. Updated the text to reflect the updated graph.
I just went in and manually played around with what I thought made sense. The primary consideration was what counties were nearest each other county and secondarily what the shape of the state was. I also factored in to some degree what counties were near others across state lines, but the number of counties not reflecting geographical sizes meant this was a bit challenging to keep consistent. I did my best though.
You're correct that increasing resolution to the county level can inflate the size of states with more counties. This kind of map wouldn't be appropriate for a state by state comparison at all; instead, it's more useful for a county by county comparison. It's just a different resolution of administrative boundary and there are limits to that.
A lot of U.S. data is reported at the county level and comparing across regions within or across states without worrying about the geography or shapes of different counties can sometimes be helpful. Adding population as a size dimension and filtering to a single state can also help mitigate the distortions.