It's because the weekday needs an article when you are stating a WHOLE date.  If you were stating just a specific date without the actual whole date, then you'd just say the name of the day.

Tuesday, January 6th, I was sick = Le mardi 6 janvier, j'étais malade.  WHOLE DATE

Tuesday, I was sick = Mardi, j'étais malade.  SPECIFIC DAY

Le mardi, Je suis malade = I am sick on Tuesdays.  TUESDAYS IN GENERAL.  Although, this would probably mean you are playing hookey every Tuesday.  Shame on you!  ;)