It sounds like this is what you're experiencing:
FAQ: Why does the engine sound different with the brakes on?Quote:
While idling, the engine noise (and associated vibration) changes when the rear brake is applied because the rear wheel is being clamped to the engine via the brake calipers. This allows vibration to travel through the frame via different paths, and also provides additional dampening that otherwise doesn't occur very efficiently through the axle alone.
The change in engine noise and vibration is not because of additional load being put on the engine. Stopped is stopped, and the centrifugal clutch is disengaged regardless.
Hope it helps.
(It may also help reading through the wiki,
Readme1st ! : Modern Vespa Wiki if you haven't already done so)
Edit: when you're stationary and the engine is running, you'll feel the difference through your butt and hear a slight change in tone if you switch between the front and rear brake.