The word "cockily" is an adverb that's used to describe behaviour that's overconfident or arrogant. Synonyms for "cockily" include "smugly", "brashly", "boldly", "swaggeringly", "haughtily", "pompously", "egotistically", "presumptuously", "imperiously", "superiorly", "condescendingly", and "arrogantly". Each of these words has slightly different connotations and nuances, but they all convey a sense of self-importance and unwarranted confidence. It's important to use these words carefully and not confuse confidence with arrogance, as this can lead to less effective communication and potential misunderstandings.