This is one of those verses where the Targum tells you a whole murder plot the Torah never mentions. Targum Pseudo-Jonathan on Genesis 24:33 says the meal set before Eliezer was prepared with poison meant to kill him.
Stop and read it again. Abraham's servant has ridden for days, crossed deserts, watered camels, found a bride, delivered the story — and he arrives at dinner to find a plate that would end him before dessert. The Targum preserves the old midrashic suspicion that Bethuel (Rivekah's father) tried to steal the treasure by killing the messenger.
But Eliezer does not sit down. He says, "I will not eat until I have spoken my words." Duty before dinner. The mission before the meal. He is a servant on assignment, and no hospitality — poisoned or otherwise — will distract him from delivering what Abraham sent him to say.
The Targum rewards his discipline. A few verses later we learn that Bethuel, that same night, ate the food meant for Eliezer and died by morning (Genesis 24:55 in the Targum). The trap closed on the one who set it. The servant who refused to eat outlived the master of the house who had prepared the feast.
Two teachings lift out of the story. First, that a holy errand is more nourishing than any meal — Eliezer's appetite for his mission protected him. Second, that the yetzer hara, the evil inclination, often serves itself what it had prepared for someone else. The Accuser's own plates come back around.