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Deriving from the saying: "weak tit on this mama cat" from the movie Sugar and Spice, but slowly forming into just the term "whine titty". Referring to someone being overly whiny about something, a child whose crying is over the top, etc. Someone who is being a whine titty can also just be called a "titty".
"Taylor Swift needs to quit being a whine titty about her boyfriends in all her songs."

"You can't go shopping this week? It's not that big of a deal. Don't be a whine titty."

"You're crying non stop is making me believe you're being a titty right now. Stop."
by blackfoxes February 24, 2013