and the reason for it.

"In the society of his nephew and niece, and their children,
the old gentleman's days were comfortably spent. His attachment to them all increased. The constant attention of Mr. and Mrs. Henry Dashwood to his wishes, which proceeded not merely from interest, but from goodness of heart,
***gave him every degree of solid comfort which his age***
could receive; and the
***cheerfulness of the children added a relish to his existence.***

In contrast to this; (I won't quote what Barbara already has)

"....who, in occasional visits with his father and mother at Norland, had so far gained on the affections of his uncle, by such attractions...[quote]...as to outweigh all the value of all the attention which, for years, he had received from his niece and her daughters. He meant not to be unkind however, and, as a mark of his affection for the three girls, he left them a thousand pounds a-piece.

This change of heart came to soon for too little. The narrator herself is seriously displeased, and is quite ironic when she details the qualities of the 2 parties concerned especially the second highlighted part which seems to drip with irony.

It would seem that the old gentleman on seeing the little boy hastened to ensure that some more generations will be settled in Sussex.
The father of the little boy may also have had some influence in directing the old gentleman's thoughts in this direction.