Vespas are not supposed to weep oil: that is a job for old British motorcycles and badly assembled Lambrettas. With age though, comes incontinence and after a few years you may find that your Vespa starts to leak, particularly if you make it sneeze or giggle.
The most common culprit for these oil leaks is the clutch cover. The simple solution is to remove the cover and replace the O-rings: both the large one around the outside rim and also the smaller one on the shaft of the clutch arm. What happens when that doesn’t work and it still leaks?