When Eliezer goes to Haran to find a wife for Yitchak Avinu, he stands by the well and asked God to show chesed to his master, Avraham Avinu. However, this seems unnecessary as Avraham has already promised him that God will assist him in his task of finding the perfect bride. Chesed is generally seen as an undeserved kindness, a gift from God to someone who cannot demand it. Yet Avraham has already been promised numerous descedents and that this progeny shall come from Yitzchak. Therefore it seems that all Eliezer really has to do is sit around at the well. Why does he specifically ask for chesed instead of just coming up with his test as described in the parasha and asking God simply to grant success to his efforts?
The answer seems to be in what made each of the Avos great. As Chazal tell us, each of the three had one special attribute that defined him. In Avraham's case, it was chesed while for Yitzchak it was gevurah. But this doesn't seem to tell the entire story.
We are all well aware that any one characteristic, however noble it might have the potential to be, can cause tremendous damage if left unchecked. Chesed and gevurah are no exceptions. Wielded in the right way and to the right extent, they contribute to a person's ability to serve God. Too much of each could lead people astray in the wrong direction.
What's more, chesed and gevurah are the balances for each other. A person can be kind in excess and it takes strength of character to know when kindness is not the right choice. And in reverse, a person's strength can lead to cruelty if not balanced by chesed.
We do find one episode in the life of Avraham Avinu where this comes into play. When Yishmael decides to mock the young Yitzchak and his mother Hagar gets uppity with her mistress, Sarah Imeinu, Avraham is loth to do anything about the situation. He clearly loves his older son and the thought of dealing decisively with the situation bothers him. On the other hand, Sarah has no compuctions about the right course of action. She forces the issue and God agrees with her, telling Avraham that his chesed is not the right way to deal with the situation. Sarah's gevurah carries the day.
Now we may have an answer to why Eliezer specifically mentioned chesed in his prayer to God at the well. Yitzchak, the essence of gevurah, would need a chesed to balance him out, the opposite of what Sarah did for Avraham. Eliezer, knowing this, didn't simply want a generous girl but one who was guided strongly by chesed just like his master's son was guided by gevurah. Thus he specifically asks for that trait.
This might also be echoed in one of Rashi's final comments on the parasha. When Yitzchak brings Rivkah Imeinu into his mother's tent, Rashi interprets the verse as saying "And behold, she became Sarah his mother". If Sarah had gevurah and Rivkah had chesed, how could this be so? Simply because just as Sarah's role was to be the perfect balance for Avraham, now Rivkah would be the perfect balance for Yitzchok, continued the family along in the best way possible.