How big an area does a barometer reading cover?

How big an area does a barometer reading cover?

Only at the exact location of that barometer. Conceivably, it could be different a few feet away, or perhaps a few miles. It depends upon the location and movement of nearby areas of high and low pressure, as well as changes in the air temperature; warming air makes it less dense which results in decreasing pressure, while cooling air makes it more dense, which results in increasing pressure.