I've had my Fly 125 just over a year now, and always ride with the top box on (it's one of the reasons I chose the Fly, as it came with a coloured coded top box as standard in the UK).
Today though I needed to move more stuff and rather than repack into the top box, I removed it and just kept the rear rack to bungee on to.
Riding without the top box, the Fly felt so much better! Much more nimble and agile, even a little quicker perhaps. Even with my heavy bag bungee'd on it still felt a lot better handling wise.
I'm at a loss to explain this, the Piaggio top box weights very little, and although bulky I cannot see why it would affect handling so much - some weird areodynamics perhaps?
Now I have a problem... I keep the top box on all the time as I do use the scooter as a 2nd car replacement, and carry quite a bit for work, but really 8/10 days I don't need it. Perhaps a fabric bag to store under the seat until needed is the way to go (and I rather like the look of the scoot with no top box and just the rack).
Hmmm....
Hewesy