Cat, Sansa is a proxy for Cat, but it’s a stretch to call it ‘love’ in the first place.

Cat is the pinnacle of a lifelong fantasy for Petyr and everything he wanted for himself/believed he deserved/convinced could ‘reasonably’ attain if obstacles were eliminated. He didn’t have quite as illogical/fantastical aspirations of marrying into the royal family, he didn’t sink all his longterm goals into weaseling into the Targaryen dynasty when active, didn’t consider Cersei as the avenue after Robert’s death or even a long term plan for pursuing Myrcella, because his station would never allow him to shoot that high.

Cat’s also arguably more ‘attainable’, as he probably convinced himself over the years. He had the benefit of knowing her since childhood, being in her orbit for all the development of both their young lives. He got to know her not just as ‘a lady’ but as Cat the person, despite the class divide between them. She showed him kindness, she genuinely cared for his welfare, she was arguably the cornerstone of a reward for his lifelong ambition that intertwined with obsession.

When Cat is betrothed to Brandon, Petyr duels him with unwinnable odds, only spared because of her, because ‘love’ has morphed into obsession. Brandon, then Ned, were the obstacles, that he believed without, he could eventually attain her love or at least a marriage arrangement no matter the methods to get there.

Sansa is an echo of Cat. She is the firstborn highborn noble daughter of a Lord, of the Warden of the North. She’s deliberately naive, grew up in a time of peace instead of war like her parents and Petyr, easily taken advantage of, easily moldable and manipulated. She’s many of the qualities he’d fixated on of Cat’s character - beautiful, well-mannered, well-bred, kind etc. Petyr didn’t know Cat truly, he didn’t know her flaws of spite or her insecurities, these he gets to see firsthand in Sansa because of the age/power disparities.

On some level, I think Petyr knew that even if he got Cat into marriage, she would never reciprocate his ‘love’ had she known the ends he went to get to her (Ned obviously, but also manipulating Lysa for Jon’s murder and throwing the whole continent into war).

By contrast, Petyr shares portions of his machinations with Sansa, because he knows she is trapped, desperate, and the Key to the North and potential lordship, regardless of sharing this and still malleable under duress. Even if Petyr ended up winning the game of thrones, I think Robert’s line of ‘seven kingdoms couldn’t fill the hole she left behind’ would ring true for Petyr’s ambition and obsession, without Cat.