Rabbi Soloveitchik claims that Eliezer was looking for more than Chesed as the character qualities necessary to be worthy of being Yitzchak’s wife. He was particularly looking to see how Rivka was when it came to הכנסת אורחים, welcoming guests.
In Parshat Vayeira, the Rav said that giving צדקה shows sympathy while הכנסת אורחים shows a certain equality with the guest.
He expands this idea in חיי שרה by explaining how welcoming guests presents different challenges. The first is that having guests in our home requires a great deal of patience. We are to be generous in sharing all of our possessions with our guest. A second point is that having guests in our home means having strangers in our home. We need to be more on guard knowing these visitors are with us. And the third point is that we need to welcome these guests while they may have strange mannerisms and opinions.
Eliezer set the bar pretty high for Rivka, but she passed with flying colors.