In the series, we see that Wade has some self-esteem issues due to people seeing him as a joke and his bowling team kicking him out. Knuckles is kind enough in his own serious, honor-bound way to help him out and train him.
Wade: Thanks for believing in me, Knuckles. Most people think I'm... just kind of a joke. Knuckles: I do not make jokes, Wade Whipple. I make... warriors.
Knuckles and Wade's friendship as a whole. Especially considering the last time Knuckles tried to find a human friend in Robotnik, he suffered a nasty betrayal. But now, Knuckles has gotten himself a true human friend who is undyingly loyal to him and has taught him how to enjoy life on Earth.
Wade and Susie's friendship. At the start of the series, she's a typical bratty girl who gleefully insults Wade. After he proves himself, she starts to respect him more to, by the point of the final episode, they're happily enjoying their bowling victory together.
Episode One: The Warrior
After a distressed Maddie asks Sonic what they should do with Knuckles, Sonic tells her that he needs time to adjust to being on Earth by being patient and understanding of his new life just like Tom and Maddie gave Sonic love and patience. Maddie is beaming at how mature Sonic has become.
Sonic: Knuckles is just having a little trouble adjusting to his new home. It wasn't easy for me to understand this planet at first, either. Maddie: When did you start getting so wise? Sonic: I read a lot of cereal boxes. Also, I had a family that was patient enough to let me figure things out. So, we have to do the same with Knuckles. Let me talk to him, when the time is right.
Before that, while apologizing to the repairmen, she outright refers to Knuckles as one of her and Tom's kids.
Tails telling Ozzy to come and calling him "Good boy", just like any dog owner would.
Episode Three: The Shabbat Dinner
Wade's mother, Wendy has spent multiple Shabbats alone, and after Wade and Wanda get into an argument that ends with them both leaving the table, Wendy looks at Knuckles and tells him that she isn't alone for this Shabbat, having Knuckles by her side.
During the dinner scene, we learned, that Wendy is a self-defense instructor, and we can easily see that Knuckles' (and the audience's) respect for her immediately increased significantly. Well, pretty much the entire conversation between Knuckles and Wendy at the dinner table, is one big Heartwarming Moment.
Episode Six: What Happens In Reno, Stays In Reno
Wade's speech to an unconscious Knuckles during his battle against the Buyer, about how the echidna made him a stronger person. It ultimately gives Knuckles a Heroic Second Wind, just as Tom's speech did with Sonic back in the first film.
Wade: Knuckles, I hope you can hear this. You taught me how to stand up for myself and fight! And we're stronger than ever now...! Because we fight together! A warrior's true strength comes from their heart! And your heart has never been bigger! You fight to honor your family! You fight to protect your friends! And now, you have something new to fight for: A home!
