Angel di Maria squared for Adrien Rabiot to made it 2-0 on 35 minutes.
Weah, 18, the son of ex-PSG and AC Milan forward and Liberia president George – struck in the final minute.
The US international, who came on as a late substitute, had scored his first senior goal for the club in the French Super Cup last week.
PSG were without their World Cup winners – including Kylian Mbappe – for German manager Thomas Tuchel’s first league game in charge of the defending champions.
Italian keeper Gianluigi Buffon, making his debut for the club at 40 after his move from Juventus, showed lightning reflexes to prevent Thiago Silva scoring a spectacular own-goal just before half-time but was otherwise a virtual spectator.