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1) Upon first meeting, all the other dwarfs are absolutely delighted at having Snow White stay for them and keep house for them. Grumpy is not. We assume he's just being 'grumpy' and hesitant to accept change. He refuses to follow orders from Snow White, too.
2) The first night Snow White spends in the dwarfs' cottages, she says a goodnight prayer which ends in, "Oh, and please make Grumpy like me." Why? Did Snow White have some strange need to please people and have their approval? (That wouldn't particularly fit in this telling of the fairy tale as even when the Evil Queen and Snow White's stepmother made her dress in rags and work as a scullery maid, she still seems oddly content. To be content in a position such as a scullery maid would not make any normal person feel such a way. At least not in the Disney Princess universe.)
3) As the dwarfs are leaving for work in the mines the next morning, Snow White kisses all of them goodbye. All of them enjoy it, specifically Dopey, who sneaks back for seconds. Grumpy procrastinates and is finally forced into a kiss, which he doesn't appear to like.
4) When the dwarfs get word that the Evil Queen has found Snow White and attempted to destroy her, Grumpy is noticeably the first to lead the group back to the cottage to rescue her. (Maybe he didn't dislike that kiss as much as he lead on...)
5) Moments before the Evil Queen disguised as a witch comes to the cottage to lure Snow White with the poison apple, she is seen making a pie for Grumpy with his name on it. Buying a man's love with food. Very coy of you, girl.
6) When Prince Charming comes riding through the forest, awakens Snow White with a kiss and asks her to leave with him to be married, she says goodbye to all the dwarfs. However, we distinctly hear Snow White say, "Bye, Grumpy!" And Grumpy doesn't exactly appear to hate the woman anymore either. He's just as affectionate as the rest of them.
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And, as by evidenced by the photo above, I'm not the only one who's noticed this before. (Although I don't entirely agree with what the photo says. Ah, Tumblr.)