Dick is proud of his position as the Big Brother of the Batfam. He likes being the one everyone knows they can come to for support and a listening ear. It feels good to think that he's the sort of person that his family can rely on. And he counts this as especially important for new additions to the family. This whole life can be... overwhelming - both the rich civilian day life, and the vigilante night life. He's been at this the longest, he has the most experience - it's only natural that it would be his role to make the newcomers feel welcome, to make the transition as easy as possible.
Which just makes it feel all the worse that he's really struggling with you. It's not your fault, not really. But he's having a bit of a tough time.
Bruce went and adopted the Joker's kid. Nobody had even known the Joker had a kid. Heck, Dick would be inclined to think you'd just been a hostage or something, except... well, there was no denying the physical resemblance. You looked like your father. Especially the eyes. How many times had Dick seen those eyes, full of malice and cruelty, looking at him like a cobra eyeing its prey right before it strikes?
You don't have the malice. He hates that he has to force his brain to not add 'yet' to that sentence. You make him uneasy, and he hates that, because let's be honest - that's a bad path. Treating you like you're doomed to become your parents and your fate is a foregone conclusion is only going to be a self-fulfilling prophesy. You've got a chance. It's up to them as your new family to give you that chance.
He wishes it were going better. Most of the fam have no clue how to interact with you, Jason's a mess and making everything worse, and Bruce is just trying his best to treat you like you're any other kid he'd taken in but not actually addressing the issues here. And Dick, well... he supposes he's sort of doing the same, isn't he? Trying to act like this isn't hard.
"Hey kiddo, there you are." He rubs the back of his head awkwardly. "Hiding out again?"