Belle decides to break things off with young Ebenezer Scrooge because of his single-minded obsession with making money. This is the moment in Scrooge's life when he started becoming the mean, grasping miser that we meet at the beginning of the story.
In breaking things off with Scrooge, Belle is completely frank. She tells Ebenezer that an idol has displaced her, “a golden one.” Scrooge replies by arguing that “this is the even-handed dealing of the world.” The world is hard on poverty as it is on nothing else, yet at the same time, it condemns the pursuit of wealth with such severity. Either way, Scrooge can't win. On the whole, then, it's better to pursue wealth than to be poor.
But Belle's having none of it. She tells Scrooge that she's witnessed the gradual falling off of all his noble aspirations until just one master-passion remains: gain, in which Scrooge has become completely engrossed. Belle was much happier when they were poor, when they were in a position to improve their lot through “patient industry.”
But Scrooge was a whole different man in those days, and Belle doesn't like what he's since turned into. And so she concludes, with a heavy heart, that there is no longer any future for them as a couple.
Dickens provides the reader a glimpse into Scrooge's past relationship with Belle in stave 2 when he is visited by the Ghost of Christmas Past. The Ghost of Christmas Past takes Scrooge back to the prime of his life to the exact moment Belle ends their relationship. Belle tells Scrooge that a golden idol has replaced her and feels that he will be happier pursuing money than remaining devoted to her. Belle recognizes that Scrooge is no longer the man he once was when they began dating and that he is solely focused on his career and amassing wealth.
The golden idol that Belle speaks of refers to the money that consumes Scrooge. Scrooge responds to Belle's allegation by stating that it is "the even-handed dealing of the world" and champions the pursuit of wealth to avoid crippling poverty. Belle understands the gravity of Scrooge's avarice and recognizes that she is no longer his main priority. In Belle's opinion, Scrooge is only concerned with the "master-passion, Gain" and does not value her like he once did.
Belle also sees her life moving in a different direction and is no longer in love with Scrooge. After commenting on Scrooge's "changed nature" and "altered spirit," she asks him if he would seek her out and try to win her heart again. Scrooge replies by asking Belle if she doubts his love, but she knows that he would not pursue her, because she is a dowerless girl with no money to offer. Belle then ends their relationship by gently releasing Scrooge of his duties and wishing him a happy life.
In addition, Belle also seems to intuitively understand that, if she marries Ebenezer, he will never truly value her. He asks her in what way he had ever sought to be released from their engagement, and she says,
"In a changed nature; in an altered spirit; in another atmosphere of life; another Hope as its great end. In everything that made my love of any worth or value in your sight."
Ebenezer has not explicitly stated that he wishes to end his relationship with Belle, but the way he seems to privilege money over everything else—including her—makes Belle realize that, in marriage, he will not find her love to be a worthwhile or valuable treasure. He has eyes only for one treasure: gold. I think it is fair to extrapolate an idea of Belle's own sense of self-worth; Ebenezer may not know her value anymore, but she knows her own. She understands that they now have different goals in life, goals that are incompatible. She will not settle.
Furthermore, she tells him, "I release you. With a full heart, for the love of him you once were." In other words, she no longer loves him. She says that she loves the man Ebenezer used to be but is no longer. He has changed too much, while she has remained the same. It was not this new Ebenezer with whom she fell in love, and, in parting from him, she seems to admit it.
In A Christmas Carol, Belle breaks up with Scrooge because he has become obsessed with money. We see this when the Ghost of Christmas Past takes Scrooge to the painful scene of the breakup. In this scene, Belle tells Scrooge he has changed, and challenges him to say this isn't so. Don't you now value money much more than you did, she asks? He agrees that he does but sees it as a sign of maturity. Belle disagrees, saying he is far too obsessed with wealth. She insists that he has replaced her with an "Idol ... the golden one" of money. He responds that poverty is the worst fate that can befall a person. Belle then says that Scrooge "fear[s] the world too much."
Belle goes on to communicate that she knows, if he had a choice now, Scrooge would never get engaged to a dowerless [meaning she brings no money to the marriage] girl like herself. She tells him he will "regret" having married her after the fact, and so she releases him from his engagement.
During his visits with the Ghost of Christmas Past, Ebenezer revisits a scene involving Belle, his beautiful ex-fiancee. In the scene, Belle accuses Ebenezer of loving money more than he loves her. When Scrooge is not able to appropriately and convincingly counter her accusation, Belle releases Ebenezer from their engagement.
To add insult to injury, while the Ghost of Christmas Past concentrates primarily on events in the more distant past, he does give Ebenezer a glimpse into Belle's more recent life. Here, we see that Belle has indeed gotten married and is surrounded both by a doting husband and loving children. Ironically, Ebenezer happens on the scene just as Belle is recounting details of her past love with Ebenezer and her husband is musing that Ebenezer must be lonely now that Jacob Marley has died.