The significance of an heir was to keep the family’s wealth confined to the family, thus avoiding it falling under the control of someone else. In addition, the idea of assigning one heir was to avoid breaking the house and devaluing the family property.

In this specific instance, Sir Walter Elliot is a Baronet, which is a title given to the wealthy. Breaking his estate for each of his daughters would dilute each of their individual wealth. The baronet title would dissipate, as there is no longer a great estate led by one man for it him to claim the title.