What is the wether typically in March the first two weeks?
Nobody really knows, weather can vary a lot from one year to another. For long range weather "forecasts", we refer people here: http://www.wunderground.com/tripplanner/index.asp input La Spezia (nearest town to CT with historical weather data) and your dates.
We were there in late March several years ago. It was cold & windy. The rest of our Italian travels were Spring-like that week.
You'll still enjoy it.
out of season. You can get answers to many basic questions by looking at the FAQ sticky at the top of the topics list. Happy planning..