A full sized keg of beer.
Full kegs contain 15.5 gallons of beer, which is exactly 1984 US fluid ounces.
Thus, "Big Brother" is a reference to George Orwell's book "1984", as well as a descriptive nickname for the beer container -- similar to "Tall Boy" (a tall, narrow 24oz beer can).
Hobo 1: Wanna go get some tall boys?
Hobo 2: Yeah, but why don't we get a Big Brother instead?
Hobo 1: Cause we're broke-ass hobos.
Hobo 2: Oh yeah, huh.