If you describe someone as unbalanced, you mean that they appear disturbed and upset or they seem to be slightly mad. I knew how unbalanced Paula had been since my uncle Peter died = disturbed
If you describe something such as a report or argument as unbalanced, you think that it is unfair or inaccurate because it emphasizes some things and ignores others. UN officials argued that the report was unbalanced. unbalanced and unfair reporting. = biased balanced