Ron liked Harry. Harry Potter's fame wasn't even aknowledged by the boy himself so he didn't act like a royalty . The boy was funny and his humour always printed Ron's smile everytime he heard one of his sassy responses. Harry was sometimes so clueless and had so little to be happy about , Ron couldn't help but pity him.
So he wanted to be friends with him. For real. But not best friends. Harry Potter should be best friends with known and respected wizards, like Malfoys. The rich and fancy Malfoys. Not the poor and freckled Weasleys.
Is just, Harry seems he doesn't want to let Ron go.