Sefer Beer Mayim Chaim writes at length about the mitzvah of gemilus chasadim and says that there are two types of people who do chesed.
The first type of person is referred to as a "baal chesed". Chazal (Shabbos 104A) describe such people as those who run after poor people in order to help them. Their hearts drive them to assist those in need, and they constantly look around for people in need of assistance so that they can come to their aid. Regarding such people, the pasuk states (Mishlei 21:21): "One who pursues tzedakah and chesed will find life."
The second type of person is known as a "baal rachamim". Such a person does not run after poor people to ask if they need help, but if he happens to bump into a person who is clearly in need of assistance, he will help him. He doesn’t seek out opportunities to do chesed, but if they present themselves to him, he does what he can to help.
There is a big difference between these two groups of people. A baal chesed will always have a house full of people benefiting from his largesse, as he will make it his business to find those in need of a meal or any form of help. A baal rachamim, however, may not see anyone in need of assistance, so his home may be empty of guests, as he doesn’t take it upon himself to go out and find them.
Chazal say (Megillah 12B) that Hashem treats people the same way that they act. Thus, He will run after a baal chesed in order to do chesed for him. Even if such a person does not daven and ask Him for his needs, and even if he isn’t even aware of what he needs, Hashem will seek him out and provide for him in a wondrous manner. When it comes to a baal rachamim, however, Hashem will help him only if he comes to Him and tells Him what he needs. He will not seek him out without him asking for assistance.
Another difference is that if a baal rachamim is approached by a poor man who asks for a dollar or two, he will feel bad for him and he will give him what he requests. A baal chesed, however, will go well beyond that. Since he wants to do as much chesed as he can, he will give the poor man much more than a dollar or two.
Avrohom Avinu was a baal chesed. Throughout his life, he pursued opportunities to welcome guests and help them in any way he could. He sat by the gate of his tent (Bereishis 18:1) in order to find guests whom he could do chesed for (Bava Metziah 86B).
Since this was his outlook on life, he tested Rivkah to see if she too was a baalas chesed and was worthy of joining his household. He told Eliezer to ask her for a little bit of water to see if she would offer to give even more than that, which would be a sign that she is a true baalas chesed.