안녕하세요! It's Koreanstudyjunkie here.
There's a lot of different text slang in Korean and ㅠㅠ/ㅜㅜ is just another one of those.
ㅠㅠ is meant to symbolize two eyes with tears pouring out. It could also be ㅜㅜ instead although ㅠㅠ is the most common. Think of it as adding a crying emoji to your message while texting a friend.
I'll leave a link to a post on interent slang here, If you'd like to learn more
Koreans have a unique way (from English speakers) of communicating feelings using only text.
For example, ㅎㅎㅎ is hahaha. So is ㅋㅋㅋ (if you are into livestreams you may know this as kekw). You can even communicate a big amount of laughter with ㅍㅎㅎ (puhaha).
They can seriously shorten words sometimes when texting. For example, ㄱㅅ (instead of 감사합니다).
Koreans abbreviate a lot of words - I'll leave a link to my abbreviated Korean words post as well.