The idiom feel a bit under the weather means to feel slightly ill or suffering from a hangover. This expression presumably alludes to the influence of the weather on one's health. [Early 1800s] The same term is sometimes used as a euphemism for being drunk.
Example 1: I feel sort of under the weather today.
Example 2: Whatever I ate for lunch is making me feel a bit under the weather.
Example 3: She said she was under the weather and couldn't make it to the meeting.
Example 4: It's hard to keep working when you're under the weather.