I’m going based off the assumption that you’ve read the books, although if you’ve only seen the show and only read the first two books, that might just explain why the Petyr/Sansa ship is a bit of a mystery to you. I included an excerpt from A Storm of Swords at the end of the post and a lot of this includes spoilers so errr. Yeah. Just FYI.
Also, let me add that I may not be the best person to talk about this ship since I am so unbelievably biased. Sho might be a better person to consult since she didn’t ship it before, but now she does yet her endgame is Petyr/moon door.
Anyways. Onwards to my unfortunately long ramble about Petyr/Sansa which consists mostly of me defending Petyr.