In the Cratchit family, Tiny Tim is the deal breaker. Scrooge has an affinity for the boy and his condition. In learning that the boy will certainly die, Scrooge finds compassion in his heart.
Fred's family is a connection..... a connection to the sister Scrooge loved, to happier days, a connection to someone who loved him very much. All of the things that Scrooge loved about Fan are present in her son, Scrooge is merely too jaded to look for them. When the ghost brings Scrooge into Fred's home, Scrooge is filled with memories of fun and happiness.... of family. As a result, the connection grows stronger.