As others have noted: you are limited only by what you can carry. That means: in Rome, if you have a taxi drop you at Termini rail station, you will have to carry the bags, unaided, down a long central corridor, then out what might be 200 or more feet down the train platform, then up three steep narrow stairs into the train (while surrounded by lots of other people jostling to do the same), then move the bags down a narrow corridor in the train carriage to your seat. When you arrive in Florence, reverse this process. Note that when you book seats on a fast train (“freccia”) between Rome and Florence (Roma and Firenze on the website or app), you will have an assigned train car (carriage) and seat. The carriages’ numbers are marked on the side of the cars. Be sure to enter your specific carriage so that you don’t have to try to move those bags through multiple cars.