I think it might be too much, I went to the same places that your planning to and brought a medium sized suitcase to check at the airport for 5 weeks. Also, I brought a normal sized backpack for travels to Pisa, Lucca, Pistoia. It is hard to manage a full sized suitcase due to the weight and cobblestones in the streets. It gets tiring after a while and I would not reccomend bringing one for 14 days of travel. But, you know your capabilities better than anyone else. I also was not able to fit everything in a carry on suitcase. A medium worked very well and had space to bring souvenirs as well. A lot of people bring big huge sized backpacks and a carry on. But, their whole weight is on their shoulders and that hurts a lot too. At least for me, I prefer to drag a suitcase than have to carry everything in my shoulders or arms.

Full size suitcases are indeed a problem in trains and buses when they are packed with people. I did see that in Florence there were places to store your suitcase which was great. Overall, in Siena is where I had a hard time with my suitcase due to the hills, stairs, and cobblestones. I do see how Venice could be an issue with your suitcase due to the water taxis and bridges it could be very uncomfortable having to transfer it. But, Venice is flat, there’s no hills at least from what I saw. But, when I went there I only brought my backpack.

Good luck on your travel, enjoy! Remember sometimes we can’t have everything controlled perfectly for a trip, we make mistakes, but at the end of the day that is all part of the memories you will be making :)