Bigger was a thug under the employ of crime lord Carmine Falcone.
While unloading shipping containers at the Docks, Batman arrived to apprehend Falcone. After he picked off the first thug, Steiss, Bigger call out to him. After Batman had thrown one of his Batarangs, Bigger picked it up to inspect. He then saw Alfie looking up, and said "What? What the -", being cut off as Batman fell on him from a lamp post.
Bigger, along with several of Carmine Falcone's other men, and Falcone himself, was left for pick-up by the GCPD.