The Jews continued to use their religious calendar for everyday use under the Roman Occupation. Six days were just called 'First day', 'Second day', etc, with only the seventh day having its own name, and being special: the Sabbath. (The origin of the word is probably Babylonian, and dates from that Exile.) That gave them the seven-day week with a regular weekend that is so familiar to us that we tend to think of it as universal. As no work, including cooking, could be done on the Sabbath, the 6th day was the logical one for major food-shopping and food-preparation.
The Romans had neither weeks nor weekends. They had, as we do today, months of varying length that did not coincide with the moons, but they did not subdivide them into weeks. Instead, individual days were deemed lucky or unlucky, workdays or holidays, or holidays for some people but workdays for others, and other complications that required priests to post calendars in public places to tell people the quality of the individual days of the next year. The Kalends (first day of the month), Nones (fifth or seventh, depending on the month) and Ides (thirteenth or fifteenth) had names as being particularly important, and the other days were counted forwards or backwards from them, but you couldn't tell much about them just from that fact.
But the Romans did have a regular market day, standardized throughout the Empire, once every eight days. This was a legal requirement; and no legislation could come into effect until it had been publicly posted for three consecutive markets.
Unfortunately, throughout the Roman province of Palestine, that meant that once every seven market days no practicing Jews would show up because it was their Sabbath. Farmers wouldn’t sell food, craftsmen couldn’t buy supplies and wouldn’t sell products, Jews would refuse to shop for the next week, and the Romans couldn't buy anything from the locals. Then they each blamed the other for being inflexible!
Any Jews who chose to attend the market on those days were seen as renouncing their religion and becoming traitors to both their people and God – and the Zealots had no more qualms about killing them than about killing Romans.
Any Jews who refused to perform normal market duties on the Sabbath were seen as actively resisting the Roman attempt to bring uniformity, progress and stability to the whole Empire, and risked being labeled as hostile.
The attempt to impose the Roman calendar on the Jews was one of the key, and constant, flash-points, from the time of the Roman conquest in 63 BCE to the destruction of Jewish life in Palestine after the Bar Kokhba revolt in 135 CE.