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
It’s especially important that she never ever ever blames Harry. She knows how he’s treated. She knows his family treat him like a monstrous freak who is responsible for everything bad that happens to them. She knows he’s been on the receiving end of anger his whole life.
She makes sure that this child (who was pretty much emotionally and physically abused for all of his young life) knows that he is not going to be harmed or shouted at or abused in her household.
She may be angry with her sons, but she knows children well enough to know how to treat Harry kindly.