From peri (around, beyond) and ergazomai (to work). To work around or beyond what is proper — hence to be a busybody, to meddle in others' affairs instead of attending to one's own.
Paul addresses this vice directly in 2 Thessalonians 3:11: some were 'not busy; they are busybodies.' The wordplay in Greek is striking: instead of being ergazomenous (working), they are periergazomenous (overworking boundaries — meddling). Idleness breeds interference. The remedy is honest work and minding one's own business (1 Thessalonians 4:11).