Simple this one, from 1731, it just puts together big and wig, in reference to the imposing wigs formerly worn by men of rank or authority.
In more detail - The term bigwig originated in the 17th century, when the short lived fad of wig-wearing (1) was at its peak. It became fashionable for people to shave their heads (2) and replace their hair with wigs; in this way they could sport a style they might not be able to naturally grow. It was seen as a triumph of man’s ingenuity over nature. However hair to make up these wigs was quite rare and expensive. Hair was sold by the strand and it was not uncommon for the lower classes to be seen wearing wigs consisting of only several strands of hair. The rich folk on the other hand were able to purchase large wigs made up of thousands of strands of hair and very soon the term ‘bigwig’ became associated with the very wealthy. This fad faded away as quickly as it had come with the advent of the top hat, however it lives on in the large ceremonial wigs seen in the British courts.