I noticed that with ITA airlines, the carry-on size that is allowed is 1/3 of an inch smaller in height and 1/4 of an inch smaller in width than the standard 22" x 14" x 9" bag allowed on American Airlines. Have you had issues with the standard 22" bag when connecting from an international flight into Rome and connecting on to Palermo? Weight of 8 kg (17.6 lbs) might also be an issue. Do they weigh the bags at the gate?
You cannot generalize from one experience but will share anyway.
I flew through Rome to Athens on ITA. I had a 22 inch carryon. It may have met the weight restrictions as I had sent home a bunch of stuff with my husband before I went onto Athens for a conference. We had been in the mountains and I did not need the warmer clothes and hiking shoes I had brought in Athens.
No one weighed my bag on either flight.
Sizing and weighing of bags is very random. I have stood in a check-in lines where every bag was weighed. Once in line where I had to remove my jacket and throw it on top of my bag -- total weight. At the gate I have seen bags reviewed and forced to check. It just depends. I always try to be as close as possible. A quarter or third of an inch is not going to make much difference. A better question is does it look too big.
Last September we flew from Rome FCO to Bari on ITA in coach. Both my spouse and I have the Rick Steves Rolling Carry-on bags (which are 21" x 13.5" x 9", so below the published size limits for ITA). Don't have an exact figure but I' pretty sure my bag was heavier than 8 kg.
Our bags were not measured nor weighed. I did not notice anyone else's bags being measured or weighed, either - but as was pointed out above, what happened to someone else on a different day is not a reliable predictor of what will happen to you.
Flew ITA last Fall. Nothing was measured or weighed. Our carryons were 10kg each.
The most severe case I have ever encountered was 15 years ago or so leaving Prague on Delta to Chicago. At check-in everything was weighed and measured and a red tag was attached to each piece. As we were standing in line I noticed a family of six (4 young kids) pushing a duffel bag under some seats - kind of making it out of sight. Later in the gate area noticed the same family but now with the duffel bag but no red tag. It looked a little large for the permitted carry on, maybe a bit long, and maybe heavy. They were ahead of us in boarding and noticed that Dad was carrying the bag low and in the middle of the mob as they were boarding. Suddenly a gate attendant grabbed his arm and pointed to the bag. I heard parts of a conversation around. " It was approved." "Tag must have fallen off" "No tag, no boarding" "Find the tag" "One of the kids must pulled it off" "No tag, no boarding" "Go back to the check-in counter." We finally shuffled past them and board. I looked for them on the plane and didn't see them. Later in Chicago, going through immigration we never saw the family again. I assumed they missed the flight.
We took an ITA flight from Rome to Venice in November. We uncharacteristically checked our bags because I was worried about the limits on ITA. I need not have. No one looked twice, and there were MANY very large "carryons" on that flight. It was a typically Italian experience, so pack your patience.