Carmy doesn't know Sydney but he knows her, and what I mean is he knows how Sydney responds emotionally, especially around vulnerability or discomfort.
Sydney pleads with Carmy not to tell anyone about the possibility that she may lose her dad. You would think it's work-related that she doesn't want her coworkers to know. Instead, it's about not wanting people to make a big deal or display of worries.
Later on, Carmy declines Richie's idea to send a gift basket to Sydney and her dad. While Richie believes Carmy is simply dismissing the idea, the truth is that Carmy knows Sydney. He understands that Sydney does not want that kind of sentiment, which is why he chooses not to go along with the suggestion.
There's trauma imprinted in Syd seeing people give so much attention to the loss of her mother and the worrying. She hates the big flowers, big displays of funerals, and the constant reminder that it isn't okay. I'm guessing that if Sydney acknowledges to people that it's not okay, she will collapse and won't get back up. It's why she has to keep going.
She may not share this with everyone, and it’s something that people often overlook, but Carmy notices. Even though Sydney still has some walls up, Syd still nearly lays herself bare enough for Carmy to feel concerned. For everyone else, bringing flowers and balloons isn’t necessary, and Carmy will make sure it doesn't happen, but Carmy wants that role for himself.
