Originally, Stephanie had no weapons. She couldn't afford any. She did appear to be in possession of some sort of grapple line for transportation, but often simply used objects around her as weapons.

Once she became acquainted with Robin, she got smoke bombs, flash bang grenades, a grappling hook, and spiked jacks she once used to take out some tires on a truck. She also apparently acquired a wakizashi, which she used to cut some power lines once.

After she got acquainted with Batman (Robin # 87), he gave her the entire Bat-arsenal, a kevlar costume, night vision lenses, del-cel jumplines, a grapple gun, smoke bombs, as well as a shurikin and bolo knives. She used a batarang one time as Robin in Batgirl #53.

Upon her return, she has these weapons, but has also been seen using a bo staff and a silver weapon (possibly a shuriken?) she deflected a knife with.

As Batgirl, so far she is not only in possession of a brand new extendable bo staff, but also has a full arsenal of batarangs, including an electrified one she used to shock a drug crazed cop into unconsciousness.