Harry was the favorite kid and he wasn’t even an official part of the family
Because Molly knows exactly how the Dursleys treat him. There’s no way Ron wouldn’t tell her. And Molly Weasley is a Mother. She gets a capital M because she is goddamn phenomenal at what she does. When she hears Harry Potter is on the train to Hogwarts in Book 1, her reaction isn’t to be starstruck. It’s to say “that poor dear had to come here all on his own.” Molly Weasley loves harder than anyone. She loves like it’s her sole reason for being. And when she hears there’s a poor boy who has never known love his whole life… how could she not?
In Year One Molly Weasley knit Harry a Weasley family sweater and made him homemade chocolate so he would have something to open on Christmas DON’T TOUCH ME
could I also just add that kids from abusive households tend to assume that yelling is directed at them and/or it heralds something bad for them so she’s making extra sure that he knows that this is not his fault and she’s not actually mad at him.
And Harry was probably standing there thinking ‘They’re all getting yelled at because of me. It’s my fault. I’m a horrible friend.’ and Molly reassures him that she doesn’t blame him. I love Molly Weasley.
Especially when she calls Bellatrix a bitch
In the 4th book after Cedric dies and Harry is sitting in the hospital wing, there is a moment where harry is trying very hard not to cry. He looks up at the ceiling and blinks hard trying to stop the tears. Not only does Molly reassure him that it was not his fault but:
"Mrs. Weasley set the potion down on the bedside cabinet, bent down, and put her arms around Harry. He had no memory of ever being hugged like this, as though by a mother. The full weight of everything he had seen that night seemed to fall in upon him as Mrs. Weasley held him to her"
Also, if we go to the 5th book and her argument with Sirius:
"Speaking as someone who has got Harry’s best interests at heart—"
"He’s not your son," said Sirius quietly.
"He’s as good as," said Mrs., Weasley fiercely. "Who else has he got?"