At the beginning of my 3rd playthrough right now, and i just collected the 3 feathers for Petruccio. 
 
-Ezio: You still havent told me why you need those feathers! 
-Petruccio: I will.. in time. 
 
 
What do you think ?  that kid is an effing tease! 
 
Im guessing that he wanted to build something and needed some feathers

the kid dies so .............. noone knows?

" the kid dies so .............. noone knows? "

 He knew that he was going to die so he asked Ezio to collect the feathers so he could build a flying machine. Petruccio came up with the idea of a flying contraption before DaVinci. DaVinci found Petruccio's plans for the flying machine after his death so he took them and perfected the idea. If Petruccio would have built the flying machine as planned, he would have died anyways by crashing into a building. 

because he hoped that someday he would shed his weak sickly body and fly like a bird, If even for a moment.

He probally wants to fly because he's also sick and stuff and can't really leave the house.

Chances are its some Italian thing that was popular at the time, my gut is telling me it's probably flair for his clothes.
What I would like to know is why do you have to collect 100 of them? Why that number and why would she give you a cape afterwards?

"        If Petruccio would have built the flying machine as planned, he would have died anyways by crashing into a building.  "