What should I expect for weather in southern Italy April 16 - May 6?
The climate in southern Italy is similar to California.
Check the averages for the locations you will be going to.
http://www.holiday-weather.com/averages/april/i/
But most importantly check the forecast a day or two before,you go, as the weather cannot be predicted too far in advance.
For forecasts use Weather Underground:
www.wunderground.com
You could run into some rain and some chilly nights, a light sweater or wrap should do it. Pack an umbrella or buy a cheapie there.