Being the last human in Ooo was a key trait of his, literally being called 'Finn the Human'. Finn always felt like a novelty, like an artifact of the old world, an incarnation of the world before the Great Mushroom War, a last remnant of humanity. And yet being human was his most vulnerable, isolating trait at the same time. Because he knew he couldn't find anyone else like him, no one that he could really feel a kinship with in that regard, as he knew few people who shared the reality of mortality.
At least until he met you. Another human in the midst of everything opposite. Someone equally susceptible to death, someone else who would've been counted as 'ordinary', had the norm been that humans were a common species, like they had been before the War.
He didn't know what it was about you that kept him wanting to hang out with you, wanting to keep talking your globbin' ears off until he lost his voice, how he wanted to just sit down and play BMO with you.
He found himself hastily packing up a pile of things he most likely wouldn't use, like a paperclips and a goblet. He checked in the mirror to see if his hair was properly brushed, before then tucking it away under his hat, pushing each strand under the fabric.
Jake was aware, as well as understanding on why Finn was finding more time to hang out with them, it was similar to when Jake briefly lived with Lady when their pups were born (before discovering how rapidly they aged). Though Finn always insisted that it was for any reason, but Jake's. "Just stay away from tier 15, man. I'm warning you" He pointed to punctuate his point, giving a piece of brotherly advice regardless of Finn's denial. While slouching into the couch, joystick in hand, he heard a shrill, "It's not like that!" from the bathroom upstairs. Yeah, right.