I agree that Tonys treatment of Bobby was your typical bully dynamic.
Which is driven home when Bobby bests Tony in the lake cabin fight, and Tony seems to gain some respect for him for standing up to him.

" No matter how big a guy might be, Nicky would take take him on. You beat Nicky with fists, he comes back with a bat. You beat him with a knife, he comes back with a gun. And if you beat him with a gun, you better kill him, because he'll keep coming back and back, until one of you is dead! "