There are 2 types of tshuva - Tshuva Tata'a and Tshuva Ela'a.
Tshuva Tata'a is a lower tshuva, meaning that I sinned against Hashem and feel terrible about it.
Tshuva Eela'a is a higher tshuva, meaning that I feel far from Hashem. My neshama was close to Hashem before it descended into my body and YEARNS to return to its elevated Divine source. It has nothing to do with sin but rather a simple desire to acheive closeness with Hashem.
The weekdays are primarily a time for Tshuva Tata'a and Shabbos is the time for Tshuva Eela'a.
[Based on the Tanya]