To express to others your own state of hardship. i.e. lack of money, job, place to live etc. Sometimes a ploy to garner sympathy. Also used to redirect mooches to another person.
derived from the character tiny Tim in "a christmas carol"
person 1 - "hey man, wanna grab a drink?"
person 2 - "oh i can't, i'm broke, my dog died, my back hurts,,...."
person 1 - "stop tiny tim-ing me!"