"Work your fingers to the bone" means to work very hard, perhaps too hard. "Under the weather" means to be ill. So it is saying if you work too hard you might make yourself sick.
What means: "Don't work your fingers to the bone otherwise you'll all feel under the weather soon..."?
Welcome to the forum, dvandemerwe.
Note that the correct construction for such a question is "What does XXX mean?" (not "What means XXX?")
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.