Please reference links below to view historical weather averages at each of the main stops on your pilgrimage.
Note: The most popular time to travel to Italy is during the spring and fall while avoiding the hot summer months. April, May, September & October are typically the best months to travel.
Rome
https://www.timeanddate.com/weather/italy/rome/climate
Florence
https://www.timeanddate.com/weather/italy/firenze/climate
Assisi