An adverb used to emphasize that something is already the case and that an additional factor makes the situation worse or more notable; roughly 'even as it is' or 'already'.
たださえ忙しいのに、来週はさらに会議が増えるらしい。
I'm already busy, and next week it seems there will be even more meetings.
彼女はたださえ人見知りなのに、大勢の前で話すことを頼まれて困っていた。
She is shy to begin with, and she was troubled when asked to speak in front of many people.
たださえ寒いのに、風が強くて余計に冷える。
It's cold enough as it is, and the strong wind makes it feel even colder.