late 12c., bileave, "confidence reposed in a person or thing; faith in a religion," replacing Old English geleafa "belief, faith," from West Germanic *ga-laubon "to hold dear, esteem, trust" (source also of Old Saxon gilobo, Middle Dutch gelove, Old High German giloubo, German Glaube), from *galaub- "dear, esteemed," from intensive prefix *ga- + PIE root *leubh- "to care, desire, love." The prefix was altered on analogy of the verb believe. The distinction of the final consonant from that of believe developed 15c.
The be-, which is not a natural prefix of nouns, was prefixed on the analogy of the vb. (where it is naturally an intensive) .... [OED]
Meaning "conviction of the truth of a proposition or alleged fact without knowledge" is by 1530s; it is also "sometimes used to include the absolute conviction or certainty which accompanies knowledge" [Century Dictionary]. From c. 1200 as "a creed, essential doctrines of a religion or church, things held to be true as a matter of religious doctrine;" the general sense of "That which is believed" is by 1714. Related: Beliefs.
Belief meant "trust in God," while faith meant "loyalty to a person based on promise or duty" (a sense preserved in keep one's faith, in good (or bad) faith, and in common usage of faithful, faithless, which contain no notion of divinity). But faith, as cognate of Latin fides, took on the religious sense beginning in 14c. translations, and belief had by 16c. become limited to "mental acceptance of something as true," from the religious use in the sense of "things held to be true as a matter of religious doctrine."