"Pirkei Avot is so popular that many siddurim...include the full text of this book. In many communities, it is customary to read a section of Pirkei Avot every Shabbat." (source)
"It is customary to study Pirkei Avot...on the Shabbats between the holidays of Passover and Shavuot, the seven weeks of the Omer counting." (source)
"Every Shabbat afternoon, Grandpa taught us something from Pirkey Avot." (Glinert)