1. What does it mean?
ㅠㅠ is visual: the vowel letters resemble eyes with tears running down. It may express genuine disappointment, exaggerated frustration, or happy tears. ㅜㅜ is a closely related written form.
Also written or said as ㅜㅜ, ㅠㅠㅠ, 유유, yuyu
2. The nuance
Read it as an emotional cue, not usually as the spoken syllables 'yu-yu.' A grateful message can end in ㅠㅠ without being sad. More tear characters do not provide a reliable measure of distress.
3. Examples
“예약하려던 시간대가 전부 마감됐어 ㅠㅠ”
All the time slots I wanted to book are gone. :(
“내가 좋아하는 색까지 기억해 줬구나 ㅠㅠ 고마워.”
You even remembered my favorite color. I'm touched—thank you.
Sources
FluentU: Korean text slang guide
References support the meaning and usage. Example sentences are written for NoCapWiki.