What’s the weather really like in these cities?

Go to the website timeanddate.com. Plug in the name of the city/village you want. Click on "weather" and then "past weather". You will get past daily/hourly information about the weather, including humidity, wind, etc. back to 2010. There is also a two-week forecast option. I use this site to help me pack.
Humidity can make or break a vacation! Last September, we were in Paris with 95-96 degree weather but the humidity was 30+%, only. We could deal with that.

Join the cities' Facebook groups, where travelers report conditions in real-time.

Not humid at all in those time periods.

Fabulous info as always!!! Thank you so much.

Venice can feel humid but humidity in May should not be terrible. I was there last October and it was uncomfortable but not bad. The prior October, the humidity wasn't bothersome.

At the end of May, temperatures in Florence will likely be slightly cooler than Raleigh (maybe in the low 80s F). It will be less likely to rain than Raleigh, and definitely not as muggy as Raleigh, not even close.

In the north (Venice and Bellagio) it will likely be a little cooler than Florence (about 5 degrees cooler or so) with a slight higher chance of rain. Venice gets a bit muggy sometimes in July and August, but not in May/early June. Nowhere in northern Italy in May/early June you will experience the mugginess of Raleigh. Italy has a much drier climate.

Rome’s weather is similar to Florence at that time of the year, although it gets a bit muggier than Florence in summer (July and August), but not when you go.

You are actually going when the weather is best in Italy, warm but not hot, and little rain.
You can also use Weatherspark to compare.
https://weatherspark.com/compare