1. What does it mean?
스윗하다 adds 하다 to the English loanword 'sweet.' It praises a caring remark or gesture, especially a small action that shows someone has noticed another person's needs.
Also written or said as seuwithada
2. The nuance
It need not imply romance. It can also be used sarcastically, so read the tone; a considerate action alone does not establish attraction.
3. Examples
“추울까 봐 창문을 닫아 주다니 스윗하네.”
Closing the window in case I was cold was sweet of you.
“기억 못 할 줄 알았던 약속을 챙겨 줘서 스윗하다고 느꼈어.”
Remembering the promise I thought they'd forgotten felt really thoughtful.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.