How come 星 (star) is used in 星期 (week)?
In ancient China, makers of calendars tried to relate rotation of stars or star constellations with mythological deities. In fact, Chinese calendar doesn't carry the concept of week.

European names for "week days" are represented by Greek/Roman mythological deities. European creating the "week" concept from there.  

Chinese scholar use 星期 to represent week when China adapt the universal international calendar, which means the day/period of the constellation/star deity complete their "duty roster". Only Sunday 星期日/天 follow the Roman/Greek, which may be due to influence of European missionary. 


  1905年，清朝学部的袁嘉谷筹建编译图书局，后任该局首任局长，编写官定各种教材，设立了一个新机构统一规范教科书中的术语，把七日一周制定为中国自己的“星期”。 
  
  In 1905, Qing Dynasty education officer Yuan-Jia-Gu establish translation and library division for the education department to standardised technical jargon. This is when Chinese use 星期 to represent the week. 


On the other hand, Japanese is using the Roman/Greek deity to represent days, as in Europe. Japan is using 曜 that carry similar meaning as constellation/star.

Note : Johann Adam Schall von Bell(May 1, 1592 – August 15, 1666) is helping Qing dynasty perfecting the Chinese calendar.  Chinese has stronger cultural interaction with Europe than many can imagine.



(update) for those curious about Japan week days


星期一：月曜日 Monday, Máni, avatar of moon
星期二：火曜日 Tuesday , The god Tiw, identified with Mars
星期三：水曜日 Wednesday, Germanic god Woden, avatar of Mercury
星期四：木曜日 Thursday, Thor's (Jupiter's) day
星期五：金曜日 Friday, goddess Frigg, Roman goddess Venus
星期六：土曜日 Saturday, Roman god Saturn
星期日：日曜日 Sunday,   Sól, avatar of Sun