Another idea: You need the camera gear, but not the heavy bag. Find ways to transport the camera gear that are lighter, so much more of that 11 lb can be gear rather than baggage. For example, a school-type backpack is far lighter than a rolling carry-on, and you can pad the gear in something light like clothes if your camera bag is relatively heavy. If your checked luggage with the camera bag is lost or substantially delayed, well, there are plenty of camera stores with camera bags you can buy once you get there, and the bags are a heck of a lot cheaper to replace than the gear.
If you try to use the more generous Delta weight limits when boarding the Alitalia flight, there's a good chance they will ask you to gate-check your carry-on if it's over the Alitalia weight limit. When there are draconian weight limits, it's usually because the plane is a very small one, and the weight limits are there for a reason and are frequently enforced. (That happened to me when transferring from a United 777 flight to a small Croatian Air flight a couple of years back.)
P.S. Another warning on Florence: I flew through there a year or two ago. It's a *small* airport, with a lot less in terms of guidance equipment for the pilots than most airports. What that means is that if it's foggy, planes don't take off or land there. I got stuck there for several hours in fog (in January) before they finally bussed us to the larger airport at Bologna, but by then I had missed my connection in Frankfurt and had to wait until the next day for a flight home. Be prepared for a delay if the weather is foggy, and next time fly into Pisa (which has a larger airport that can handle a little fog, and isn't far away) instead of Florence!