I'm sure that the quote that you are reading refers to the Postal Rate in effect from July 1, 1851 until September 30, 1852, where circulars were rated by distance.
For circulars weighing 1 ounce or less:
- Pre-paid Under 500 miles was 1c
- Pre-paid 500-1500 miles was 2c
- Pre-paid 1500-2500 miles was 3c
- Pre-paid 2500-3500 miles was 4c
- Pre-paid over 3500 miles was 5c
Effective October 1, 1852, printed matter was rated at 1c for the first 3 ounces or less.
Because this distance-based printed matter rate was only in effect for a little over a year, and not everyone used stamps yet, these multiple rate distance-based circulars are highly sought after by collectors. I ought to know, I used to "seek" them.
2c circulars are scarce items, 3c ones are quite rare. There are probably more out there that we have not identified, since they can easily be confused by a 3c stamp simply paying the normal single letter rate -- which is clearly what your cover is.
2c circulars were almost invariably paid by two 1c stamps, and are easily identified by use in period, not overweight and the towns apart by the proper distance.
I am aware of a famous 5c circular cover from the west coast. A fantastic item.