The origin of the term "big cheese"

The big cheese is the most influential or important person in a group, though it has often been used in a derogatory way to refer to somebody self-important. These days, it’s more than likely to appear as a joking reference to a real cheese, since its slang use is rare and definitely outdated...

...the most probable source is the Persian or Hindi word chiz, meaning a thing.

The expression used to be common among Anglo-Indians, e.g., “My new Arab is the real chiz”; “These cheroots are the real chiz,” i.e. the real thing. The word may have been an Anglo-Indian importation, and it is difficult otherwise to account for it.

An expression with the same meaning that predated the real chiz was indeed the real thing, so it’s probable that Anglo-Indians changed thing to chiz as a bilingual joke. Once returnees from India started to use it in Britain, hearers naturally enough converted the unfamiliar foreign chiz into something more recognisable, and it became cheese.

Found at World Wide Words.