There are various opinions in the Midrashim regarding the heritage of Bilaam.
The idea that is quoted by 'sabbahillel' in the name of Rabbi Sacks is a Gemara Sanhedrin 105a. The Gemara also says identifies Be'or as Lavan. Bilam would therefore be Lavan's son. http://bit.ly/1GX1a4p
The Zohar identifies Be'or as a son of Lavan, making Bilam the grandson of Lavan. http://bit.ly/1LG12uj
The Yalkut Shimoni (766) says that Bilam was also known as Kemuel and was the son of Milka - http://bit.ly/1CHaGVr - which would make him the nephew of Avraham, the father of Aram and the uncle of Lavan.
The Midrash Tanchuma (Vayeitzei 13) - http://bit.ly/1NsxTAZ and the Targum ascribed to Yonatan ben Uziel (Bamidbar 22, 5) - http://bit.ly/1CHc5LD - say that Bilam was in fact Lavan himself.
In the Gemara Samhedrin 106a, Rav Simai states that Bilam was an advisor to Pharaoh in Egypt. However, on 106b the Gemara quotes Rav Chanina as stating that Bilam died in his 30s and Rashi points out that the two Amoraim disagree.
The Sefer Hayashar (Parshas Shemos) implies that Bilam ben Be'or was from Africa and he was a fifteen year old servant of King Angias when he rose to prominence. (This was 72 years after the Israelites had gone down to Egypt.) http://bit.ly/1LAztl6
With regards to the question, "Is he some kind of disgruntled Abrahamite?" we see that according most opinions, Bilam was of Abraham's family and therefore would have been very familiar with his concept of God. The Yalkut Shimoni (ibid) points out that all the prophets of the nations of the world were descendants of Abraham's brother Nachor & wife Milka (e.g. Iyov). There was a lot of potential spiritual greatness in the family, but it was channelled in very different ways.