Thumb is the biggest among our fingers, Chinese ancestors used plus "白" to mean the oldest brother among the siblings, especially brothers. We can see from "伯" that "白" does mean Thumb originally.
"伯" was extended to mean "Older brothers of a father" or "Is used to address an elder man respectfully"
Let us still examine the evolution history of "伯": ( image get from http://www.vividict.com )
|Learn one Chinese Character a day – 伯|