My wife and I are in the same predicament, we're 68 and 76. We took two pieces of small, light luggage for a trip this past May--it was something close to a disaster. No one bag was heavy, but managing two small pieces of luggage each, plus a back-pack each, plus 2 CPAPs plus my wife's handbag was, well, awful. There was just too much to manage, especially getting on and off trains, trams, buses, etc.
Based on the "small luggage" fiasco, we decided on one piece of luggage a piece, plus CPAP for "next time". We tried this on a 2 week visit from which we just returned. This was a 9-day cruise and 4 days in Barcelona on our own. We checked the bags through to our cruise destination, no hassle; until, that is, our luggage didn't arrive for 5 of the 9 day cruise. It wasn't nice as we were not in ports conducive to shopping for modest-priced plus-size clothing (e.g., Monte Carlo, Ajaccio, and Olbia (where the town was closed for Ferragosto).
We're now considering shipping our luggage ahead for a visit we are planning in early may of 2018 to Scotland.
If you have booked a hotel in Sorrento (or elsewhere on the Amalfi coast) so you know the exact location of your first destination, you may want to consider this option. Some providers charge flat rate for certain weight luggage, others charge by the pound. This way you would eliminate the luggage issue, at least until your first stop. I assume you will stay at one hotel during your time in the Amalfi area, so luggage shouldn't be a problem. Then, if you will be in Rome just "a few days", before you depart the Sorrento Amalfi area, send most of your things back via the same provider you shipped them to Italy, and take a small wheeled carry on to Rome and eventually back to the US--purchasing the small luggage in Amalfi for the balance of your holiday.