It is mentioned in Masechet Ta'anit 4 3 that people should not fast on Sunday "ולא באחד בשבת כדי שלא יצאו ממנוחה ועונג ליגיעה ותענית וימותו". ("And not on one of the Sabbaths so that they don't come out of rest and go to bed and fast and die.") There reasons are that they do not leave the pleasure of Shabbat for fasting, they will get sick and die. And also because Sunday is the third day of man's creation and on this day he is very weak. So why there are fasts (and even postponed fasts such as Ninth of Av) that occurs on Sundays and are not postponed to other day?