I agree with Kathleen that it has nothing to do with trying to get Elinor together with Edward.

The story of Edward's plight has touched Colonel Brandon and because of his own disasterous romantic past, he feels 'great compassion' for a young couple who are (so he believes) romantically attached to each other, but whom a parent is trying to force apart for financial reasons. This reminds him only too painfully of what he went through with Eliza, and is yet another example of Colonel Brandon's romantic nature. He could not save himself and Eliza then because he had no power and no means, but now that he does have the power and the means to save another couple from a similar fate, he acts--as though trying to right that past wrong that was done to him.

As he tells Elinor, "The cruelty, the impolitic cruelty of dividing, or attempting to divide, two young people long attached to each other, is terrible; -- Mrs. Ferrars does not know what she may be doing -- what she may drive her son to."