The belt could be too tight (not good for the engine). Do you have the correct belt for the bike?
The proper way to check belt tension is to measure out on top of the belt, 12.4 inches from the middle of the rear pulley. At that 12.4 inch point you are supposed to hang about 4.4 lbs weight from the top belt. The belt should have about 1/2 inch of downward play if it is adjusted properly.
If the original reason was for tightening the belt to the max was lack of power, then the main clutch shoes may be worn and need to be replaced.
While we are talking about clutch shoes, another common mistake is to install the starter clutch shoes backwards. If you have the clutch assembly off and looking down into the clutch, the starter shoes should be at the 7 oclock and 1 oclock positions, so they spin outwards properly when you pedal.
If you need new starter or main clutch shoes you can order them from the Vespa Super Shop in San Diego.
Have you ever had the clutch off? There is a little spacer that goes on the shaft before the clutch goes on the shaft. It is shaped like a little hat with a brim. A mistake people sometimes make is to put this on backwards with the top of the hat pointed toward the engine. It should be with the brim against the engine side with the top of the hat pointed outwards.
You can clean the clutch shoes with brake pad cleaner. You can also use emery paper to remove the glaze a bit and have more of a rough surface on the clutch pads. Also lighty grease the pivot points where the clutch shoes are secured but don't over do it.
Take a look at the rear pulley by standing behind the bike while it is on the center stand with the engine running and see if the pulley wobbles excessively.
Don't forget to check the gear oil in that rear hub for the final reduction gear.