When the Hobbits were still a wandering people, their calendaric unit was not a 'week' , but a 'month', governed more or less by the Moon. However though contact with alien peoples (perhaps the Dúnedain of Arnor) they adopted the notion of weeks which formed the Shire Reckoning. It was based on the King's Reckoning but with several minor alterations to fit their customs.
The calendar featured 12 months, all 30 days long, plus 5 or 6 named days added to round out 365 days (or 366 for leap years). Two of the named days were Yuledays; one was the first day of the year and the other was the last day of the year. Between June and July were the Lithedays. In regular years (not leap years) there were three: 1 Lithe, Mid-year's Day, and 2 Lithe. In leap years (every fourth year except in the last year of a century) an extra Overlithe Day was added after Mid-year's Day. All of the named days were major holidays (and a reason for feasting) with Overlithe being a day of special merrymaking. The two Yuledays were actually a portion of Yuletide, which included the last three and first three days of each year.
One innovation introduced by the Shire-hobbits was the Shire-reform. In the time of Thain Isengrim II they arranged that Mid-year’s Day (and the Overlithe) would not have a weekday name, which stopped the shifting of weekday names in relation to dates. This change made the first day of the year always correspond to the first day of the week, and the last day of the year always correspond to the last day of the week. Over time, since the same date in any year had the same weekday name as in any other year, the Shire-folk ceased to record the weekday in letters and diaries. Since no month began on a Friday this arrangement also birthed a jesting idiom in the Shire: "On Friday the first" referred to a non-existent day or one on which impossible things would occur (the full expression was "on Friday the first of Summerfilth").
The twelve months of the Shire Calendar were: Afteryule, Solmath, Rethe, Astron, Thrimidge, Forelithe, Afterlithe, Wedmath, Halimath, Winterfilth, Blotmath, and Foreyule. Solmath was usually pronounced and sometimes written as Somath. Thrimidge was often written Thrimich and Blotmath was pronounced as Blodmath or Blommath.
The seven weekdays of the Shire Calendar (at the time of the War of the Ring) were Sterday, Sunday, Monday, Trewsday, Hevensday (or Hensday), Mersday, and Highday. The last day of the week, Highday, was the chief day, a post-noon holiday and time for evening feasts.