"When Abraham's servant heard what they said, he bowed down to the ground before the Lord. Then the servant brought out gold and silver jewelry and articles of clothing and gave them to Rebekah; he also gave costly gifts to her brother and to her mother." NIV translation
Eliezer fell down and worshiped God because he knew that it was only God that had arranged this marriage and got the family to see it. He then presented gifts (the bride price) to Rebekah and to her family.
"Then he and the men who were with him ate and drank and spent the night there. When they got up the next morning, he said, 'Send me on my way to my master.' But her brother and her mother replied, 'Let the young woman remain with us ten days or so; then you may go.' But he said to them, 'Do not detain me now that the Lord has granted success to my journey. Send me on my way so I may go to my master.'" NIV translation
Abraham's servants celebrated the success of their journey and stayed the night.
The next day, Rebekah's brother and mother tried to get them to stay. We do not know why but we can guess that it was in hopes of getting more gifts from Eliezer.
"Then they said, 'Let's call the young woman and ask her about it.' So they called Rebekah and asked her, 'Will you go with this man?' 'I will go,' she said." NIV translation
Now, we see that, even though God may arrange a marriage or other event in our lives, He allows us the choice. Rebekah agreed to marry Isaac and so the matter was settled.
"So they sent their sister Rebekah on her way, along with her nurse and Abraham's servant and his men. And they blessed Rebekah and said to her, 'Our sister, may you increase to thousands upon thousands; may your offspring possess the cities of their enemies.' Then Rebekah and her attendants got ready and mounted the camels and went back with the man. So the servant took Rebekah and left." NIV translation
Rebekah's family sent her with their blessing and her servants.