Two people (so far), including myself, have commented about how this map, like many that show counties on a country-wide basis, emphasizes how counties get larger as we move from East to West.
I suspect that both the size of the states, which also grow as you move from East to West, just not always as noticeably, are factors of when the lands were divided up for governmental purposes. I once heard, somewhere, that, with three exceptions, the all of the states could be crossed in about one day by the most common method of transportation at the time their current boundaries were set. I suspect that the states were divided into counties, parishes, boroughs, etc. in a similar way. So as we move from east to west, the states and counties get larger because of the changes in transportation over time.
FWIW, the 3 exceptions are Texas -- which normally would have been 3 or 4 states -- California (2 states) and Alaska (3 or 4 states). Montana may also be an exception. I think at least two of these states were left in tact as much due to issues around the slavery debate as for any other reason. Alaska, and Montana if it should have been 2 states, were probably population density issues.