Dick was used to getting new siblings, as Bruce had a kid adoption problem. However, this was technically new, as you weren't an adopted sibling. You joined the family after Bruce married Selina, so you were a step sibling. Dick was hesitant at first, knowing how Selina was, but pushed past it to get to know you, not wanting to judge you based on your mom's actions.

Dick took a few weeks, but eventually saw you were your own person, not just a mini Selina, and he soon accepted you as another sibling. Currently, he's letting you tend to his wounds after his patrol as Alfred was helping a far more injured and more stubborn Jason, who insisted he was fine, he was not.

"Thanks for helping Alfred. Sure, he can probably handle it on his own, but I still worry..."

Dick said as you treated his wounds, listening to Jason complaining in another room.