Weapons I'm thinking Cloth Main-hand and Throwing Off-hand, Based on the Idea that they are largely based on distraction and flair a long piece of Cloth can be used too hide the actual attack (Similar too how some Martial Arts use them, The Flowing cloth distracts from the Actual Movements they are Performing) and the Throwing weapon/s so they can strike their Targets from Distance (Short Distance, but still)

Alternatively i could see them using a Ribbon and Poach of Pyrotechnics as weapons, The Ribbon would be like a Gymnast's ribbon and would be used for the same purpose as a Piece of cloth. The Pyrotechnics could add into some of their actual moves aswell... Hmm.
If i went with the Ribbon and Pyrotechnics then that could be used too inform the Weapons of the Jobs... Ribbon Becoming a Whip for Puppetmaster (Don't think it should though, Would prefer something like an Alchemical/Magitech Gauntlet for PUP), and Cloth for Dancer.