Let\'s suppose I have following Time Series:
Timestamp Category 2014-10-16 15:05:17 Facebook 2014-10-16 14:56:37 Vimeo 2014-10-16 14:25:16
Convert your TimeStamp column to week number then groupby that week number and value_count the categorical variable like so:
value_count
df.groupby('week_num').Category.value_counts()
Where I have assumed that a new column week_num was created from the TimeStamp column.
week_num