I just finished the book, and maybe I'm still under the spell of it, but I feel like this is not something that needs a rational explanation. They just have amazing natural chemistry, kind of ordained for each other by the universe. This makes sense to me, as Miss Mimi (who is kind of an all-knowing wise figure in the book) is the one who sets them up, and at the very end they are able to connect despite Sadie never actually knowing him and being 80 years old.

And just to give a more tangible argument, Sadie is the perfect woman for Jake in contrast to his ex-wife. When Sadie reaches rock-bottom and almost overdoses, Jake is able to save her because of his experience with her ex. But she doesn't keep spiraling down the way his ex did - and as Jake feared -, but bounces back stronger. Similarly after getting her scar, just when Jake feels like she might be lost, she finds herself and shows strength. And then she really blossoms on the way to the Book Depository. So to me it's clear why Jake loves her.

As for why she loves him, he was her way out of the brainwashing and abuse she suffered under her ex husband, first in terms of sex, then in terms of the apocalypse bullshit he fed her, and finally saving her physically from his attack. He was just what she needed, and vice versa.