Hi! I'll just try to answer this from my interpretations while reading parts of MB/SB/H right? So please feel free to correct any facts I might get wrong. 
Also thanks OP for allowing me to rant after a long time! 
So, in my understanding, Krishna and Arjun were both very lonely people. Both of them were stripped from their childhood homes and families, and forced to grow up amidst hostility and constant conflict, when they met after Draupadi's swayamvar, they instantly latch on to each other. I mean, yes, both Krishna and Arjun had brothers who went through the same kind of issues, but at some point, you encounter a boundary with your immediate family, such that you can't really tell them everything that you're feeling. A friend peering in from outside is a much 'safer' choice. I'd imagine it's roughly the same kind of thought process that makes people talk about their personal struggles anonymously on social media instead of with their families.
In this process, they both also become extremely possessive of each other. For Arjun, we see this when he sheds all his inhibitions at Kurukshetra not when he hears the Geeta, but rather when Krishna gets wounded the first time. That's when the Kaurava side finds out exactly how dangerous Arjuna can be. And that's when Krishna is barely scratched by an arrow, and thankfully we never find out what Arjun would have done if Krishna actually got hurt. Arjun was fighting only half-heartedly in the beginning, but once Krishna is targeted he becomes fiercer, now actually concentrating on the battle, and then finally when Krishna almost murders Bheeshma, that's when Arjun becomes fully activated, so to speak. Also, he would've totally murdered Shishupal during the rajasuya (to hell with the 100 offences), if not for Krishna stopping him...this is a rare kind of aggression for Arjun which he doesn't show even in the dice hall!
Krishna, on the other hand, shows his devotion in a slightly different way. So, for most of MB we see that he is partial to Arjuna, and he never really hides it. He gets Subhadra married to Arjuna, takes him on picnics on Kailash and shows him Vaikuntha just for fun. Moreover, he technically didn't need to participate in Kurukshetra. With Subhadra married to Arjun and Lakshamana married to Shamba, he could've easily cited an algebraic cancellation and got out of the whole mess like most of the other Yadavas. But he chooses to go to Matsya, and moreover offers to part himself from his beloved, personally trained army! I mean it was kind of genius to bait Duryodhan into thinking he won that bargain (if Shakuni mama was there, he would've definitely chosen Krishna, and immediately have him thrown in a dungeon and use him as a hostage to force the Pandavas into surrendering)!
Krishna is not just partial to Arjuna, but he is downright desperate to protect him from anything and everything. From personally waiting on Arjuna in Dwarka during happier times, to breaking every moral code he's ever stood for during the war, Krishna's love for Arjuna outshines every other horrible thing that happens.
Krishna is quite open about his decision to get Arjuna out of the dharma-yudhha mess alive. In fact, he makes it clear to Draupadi herself that if it came down to choosing between Draupadi and Arjun, Krishna would choose Arjun always, without a second thought. We see this in action when he offers to have Draupadi marry Karna in exchange for his support to Pandavas, thereby averting the whole war. We see how Krishna doesn't care how many people he has to sacrifice (Abhimanyu, Ghatotkach, upa-Pandavas, his Narayani sena, Parikshit, and borderline forcing Shikhandi to detransition, although the source of this I can't quite remember right now), how many times he has to endure the Vaishnavastra, how many times he has to make Yudhishthir lie, how many times he has to forget his vows, how many times he has to make literal celestial bodies bow to his will, all of it is taken in stride just so Arjun lives to see another sunrise. At one point, I do feel he stops caring about preserving Arjun's feelings through this (point: sacrificing his kids) and just making sure he's alive, no matter how broken or hopeless. It's almost as if Krishna's just on auto-pilot the whole time.
His whole life, Krishna asks Arjun for just one thing, which is to get the citizens of Dwarka out of the island/coastline alive before the tsunami hits. Even that, Arjuna is informed of only after Krishna is no longer on the earth. And Arjuna also is ironically one of the only people (except maybe Nand-Yashoda, Radha and gopis) to never ask Krishna for a favour! No matter how tough their life got, Arjun never asked Krishna for anything for himself. I can imagine how Krishna, the human god, would constantly be bombarded with prayers and requests literally wherever he went, so I can see why people like Arjuna would be somewhat of a relief. Even during Geeta, Arjun is like, "I can't do this!" and not "You can't make me do this!" And Krishna likewise is not like, "You have to do this!" He's just like, "You can do this, but only if you believe you can!" Krishna basically goes over all the pros and cons of the available choices but ultimately leaves the final decision to Arjun.
**I'll edit/add to this later if I can remember more dramatic stuff to add! 
Also although my signature quote is form doctor who, i can totally hear Krishna and Arjun both saying it to each other in some wilder au 
Edited by wayward - 1 years ago
Kyunki Saas Bhi Kabhi Bahu Thi 2
Geet - Hui Sabse Parayee
Cricket
