Visiting Palermo controlled large parts of the opening 45 minutes, although they were unable to break the deadlock.
Abel Hernandez had his side's best two chances, but on both occasions he shot wide from inside the area.
However, with 10 minutes of half remaining they were reduced to 10 men when Steve von Bergen was handed his marching orders for a deliberate handball on the edge of the area.
Despite their numerical disadvantage Palermo continued to look the more likely to break the deadlock after the restart.
Nevertheless, in the 88th minute Weiss converted into the top right-hand corner of the net following a cross from Giuseppe Colucci to seal the victory for his side.