This is a theory I’ve had for a while, and I’m kinda shocked that I’ve never seen anyone suggest this. And just for the record, I don’t want this theory to be true (I’ll explain my somewhat lame reason why later) but, I think it could actually be a possibility, so I must post about it.
I got this idea from the Gravity Falls Wiki on Carla McCorkle
http://gravityfalls.wikia.com/wiki/Carla_McCorkle

In the section where it describes her appearance it says “… long, curly brown hair similar to Mabel’s…”

And then it clicked. What if their hair is similar because they are related? What if, one way or another, after Carla and Stan broke up, Carla got together with Dipper and Mabel’s paternal grandfather aka, Stan’s brother? (most, if not all of you, recognize Stan’s brother as the Stan Twin Theory) Thus, this would make Carla Dip and Mabel’s grandmother.

Now consider what this would do to Stanford and his brother’s relationship. Obviously Stanford and Carla were together for a LONG time, so after they broke up, Stan would have felt very betrayed when his own brother got together with Carla. This would result in fighting and arguments between the brothers, and eventually lead to like a rivalry type thing (i feel this is an idea that is often overlooked, most of us assume that Stan is trying to save his brother via the portal, and that they had a good relationship, but perhaps instead, the portal is for something else, and Stanford and his brother could see eachother if they wanted to, they just don’t because they don’t like eachother)
Anyway, so the brothers stop talking to eachother. Then we get to the present day, Stanford is now looking after his great niece and great nephew, in other words, the grandchildren of his ex-girlfriend and his brother. If Dipper reminds Stanford of his brother, that explains part of the reason he’s so harsh on Dipper (ya know, besides the reasons mentioned in Dreamscapperers), Stanford is still mad at his brother, and is, probably unintentionally taking it out on Dipper. As for Mabel, what if she reminds Stan of Carla? That would explain why he’s so easy on Mabel. 
Now I have two sub-theories on HOW Carla got together with Stanford’s brother, for both of these its important to know that part of this theory is Stanford isn’t telling his niece and nephew what happened between him, his brother and Carla for their protection. How do you think Dip and Mabel would feel if they found out their grandfather ruined their great uncle’s love-life? Hurt.
So my two sub-theories for how Carla and Stanford’s brother got together
1. Eventually, Carla and the hippie guy broke up, and sometime after that, Carla and Stanford’s brother started going out. When Stanford told Dipper about Carla, he purposely left out the fact that the two eventually broke up, to protect his nephew from the truth

2. When Stanford was telling Dipper about Carla, HE WAS LYING ABOUT THE HIPPIE. Stanford wanted to relate to his nephew, so he told the story about Carla and how she was stolen from him, but he lied and said a hippie was the one who stole her. The person who really stole her away was his bro, and Stan simply replaced his brother, with a made up hippie when he told Dipper the story, to, again, protect Dipper from the truth

Problems with this theory: First of all, if Stan was harsh on Dipper because he reminds him of his brother, considering what happened, I’d imagine he’d be MUCH HARDER on Dipper. Also, since both Dipper and Mabel are Carla and Stanford’s brother’s grandkids, Stanford would probably be hard on both Dipper and Mabel, not just Dipper. Frankly if this theory is the case, I’m shocked Stanford actually let the twins come live with him for the Summer at all. Hmm…there was some other thing that disproved this theory…but I can’t remember..oh well..

Again, I DON’T WANT THIS TO BE TRUE. Why? My lame reason is, I love stories about family, and loving caring family moments, so I don’t want Stanford and his brother to hate eachother. Actually, I’m okay with them hating eachother right now, depending on the reason. If the men can recover from whatever the reason they hate eachother, I’m fine with it, that will just make for an adorable mushy brotherly moment later. However, a situation like drama over a woman is a family situation that is SOOO hard for people to recover from, therefore I’d don’t like it. It makes me sad 😦 over all I really like the theory that Stanford seriously cares about his brother and is trying to save him more than I like my own theory 😉
But I saw it as a possibility, so there you go!
Let me know what you guys think! Let me know if you figure out what that other thing was to disprove this theory that I can’t remember was!

EDIT: I REMEMBERED! when Stan was telling Dipper about Carla, if Carla was actually Dipper and Mabel’s grandfather, he would have recognized her name.