The key, I think, is in the words just before this:

"It was an office, in short, from which, unwilling to give Edward the pain of receiving an obligation from her , she would have been very glad to be spared herself; -- but Colonel Brandon, on motives of equal delicacy declining it likewise..."

Elinor does not want Edward to feel obliged to her. Colonel Brandon, who is only trying to do a good deed on the principle of romantic love, does not want Edward to feel obliged to him either. In Brandon's opinion, the gift of this small living with its 200 pounds a year doesn't warrant that Edward should feel indebted to him, and he thinks Edward will feel that way if he is the one to tell Edward about it.