Hand-luggage is never weighed in my experience, and you can easily carry a small bag eg. computer in addition to your main one -- it's officially allowed. For suitcases they are generally reasonably flexible. The official weight limit is 23KGS -- if you've got for example one suitcase over and one under, or if you're only 1 or 2 kgs over, that's generally ok.
( re hand-luggage: " Briefcases and laptop computers are considered hand baggage and may be brought on board in addition to the limits indicated. "
http://www.alitalia.com/be_en/Inform...bagagli_a_mano )