Their friendship would become deeper. Ron would be more protective and more attuned to Harry's emotions. There would be a new level of trust as Harry has shared such a difficult and personal experience with Ron.
The friendship would change in many ways. For starters, Ron would be more watchful over Harry. He'd be more likely to include Harry in everything he does, not wanting him to be alone. They might also have more serious conversations, and their bond would be strengthened by the shared knowledge of Harry's abuse. Ron would probably become more of a confidant for Harry, and their friendship would be based on a deeper understanding of each other's pain.