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Ever since Dipper's birthmark reappeared in "Dipper and Mabel vs. the Future," I've been toying around with an idea about the odd mark.
It's obvious that Dipper and Ford mirror each other in the same way as Stan and Mabel in terms of personality, their backstories also seem shockingly similar.
Ford's most striking feature is his six-fingered hands, a birth defect known as polydactyly As a kid, the local bullies frequently berated the odd trait, and the only person who accepted him as is was Stan. The "high-sixes" and nickname "Sixer" really seem to have helped Ford's self-esteem.
In college, Ford's extra fingers inspired his life's work: investigating the unknown. His hands became the symbol of his research; the extra finger was the only thing we knew about his appearance throughout most of the series. His attitude toward his odd appearance was completely inverted.
Dipper's birthmark is his equivalent to Ford's polydactyly. Like his uncle, Dipper was ashamed of his odd appearance. While he ended up hiding the birthmark, he never seems to have objected to his nickname. I'm inclined to believe that Mabel was the one who first called him that. She wanted to help her brother accept himself, just like Stan supporting Ford.
Another trend I've noticed is that the birthmark usually comes out during times of intense emotion: revealing his most humiliating secret to his crush ("Double Dipper"), questioning his entire relationship with his Stan ("Not What He Seems"), and nearly losing Ford to an alien craft ("Dipper and Mabel vs. the Future).
The birthmark may very well be the central theme of Dipper's future, just like Ford's fingers. Growing as a person entails learning to accept yourself for who you are. If Dipper is to follow in his Ford's footsteps, he'll have to learn this same lesson. To quote Ford:
"Listen to me, Dipper: this town is a magnet for things that are special. And that includes you and me. It brought both of us here for a purpose! Stay here with me, Dipper. Become my apprentice. Don't let anyone hold you [back]." —Ford Pines[source]