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late 14c., "customs official;" later "buyer" (early 15c.), from Anglo-French custumer, from Medieval Latin custumarius, from Latin consuetudinarius (see custom (n.)). More generalized meaning "a person with whom one has dealings" emerged 1540s; that of "a person to deal with" (usually wth an adjective, tough, etc.) is by 1580s. In Shakespeare, the word also can mean "prostitute."
A person; cookie •The word has a tinge of disapproval: a tough customer/ She's a shrewd customer
[1580s+; perhaps an expansion of cuss]