Or HaChaim on Genesis 24:17/אור החיים על בראשית כ״ד:י״ז

1 הגמיאיני נא מעט מים, "let me please sip a little water, etc." Eliezer actually asked for less than he had originally stipulated, seeing he meant to ask her "to incline her jug in order to let him drink (extensively)." Not only did he only ask to take a sip, but he stressed that he wanted only a little water. He also failed to ask her to incline her jug in order to give him to drink. Our sages (Bereshit Rabbah 60,5) explain that Eliezer saw that the waters rose towards Rebeccah. This is when he realised that she was not a Canaanite girl and that she was destined for Isaac. He became afraid that he might forfeit an opportunity by insisting on the conditions he had made in his prayer, and proceeded to ask for the minimum possible. He wanted to make it easy for the girl to meet his request.