Here's the breakdown:
* suspect (noun/verb): To have doubts about the truthfulness or integrity of something or someone.
* suspicious (adjective): Feeling or showing doubt about someone or something.
* suspiciously (adverb): In a way that shows doubt or mistrust.
So, "suspiciously" is formed by adding the adverbial suffix "-ly" to the adjective "suspicious," which in turn derives from the root word "suspect."