The 24AA00 part is only 16 bytes total. The issue seems to be with the Mouser online listing being incorrect (specifications are correct in their PDF catalog). I don't know how common this is, but it is probably not unique.
Hey if you want a decent sized well-arduino-community-supported EEPROM, I suggest 24LC256 (32KB) and 24LC512 (64KB).
16 bits for addressing is 216 = 256 addresses