I read that Alitalia has an 11lb limit for carry on bags. I guess they don't let you bring too much with that! 11lbs is not very much, do they actually check the weight of the bag?

Most of the European airlines do indeed check the weight and size of your carry-on bag. Alitalia also has strict size limitations, and they limit you to 1 carry-on bag.

I have flown Lufthansa (a lot), Iberia, bmi and Air France and have never been checked. I hear Alitalia is spotty at checking. I would imagine that if I had a standard back pack it would probably go un-noticed. It sounds like the people carrying bigger bags are singled out. Does flying biz class give me any privledges?

In most cases, flying business class gives you a lot of privileges regarding your bags. In my experience, the airlines do more careful checking in Europe than here, but my friend had to check his bag on Air France in May because it was too large. However, I can't comment on how rigid the rules are interpreted. But there are certainly rules.

We flew Alitalia (Boston to Rome) in July and they did not weigh our carry-ons. There were four of us (all adults) and three carry-ons and one laptop. They did weigh our checked in luggage but did not say anything about any of the bags being overweight. One bag was overweight a little (not mine) and nothing was said.