If you do something sobbingly, you do it while you are crying a lot.
Sobbingly is a sad word. It means someone is very sad and crying a lot.
Examples:
She said sorry sobbingly.
He hugged her sobbingly.
Sobbingly, she told him she was very sad.
He ate the cake sobbingly because it was so good.
She ran away sobbingly because she was so scared.
He said goodbye sobbingly because he didn't want to leave.