*leubh-

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 in English 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]

The 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."

Middle English bileven, from Old English belyfan "to have faith or confidence" (in a person), earlier geleafa (Mercian), gelefa (Northumbrian), gelyfan (West Saxon), from Proto-Germanic *ga-laubjan "to believe," perhaps literally "hold dear (or valuable, or satisfactory), to love" (source also of Old Saxon gilobian "believe," Dutch geloven, Old High German gilouben, German glauben), ultimately a compound based on PIE root *leubh- "to care, desire, love" (see belief).

The meaning "be persuaded of the truth of" (a doctrine, system, religion, etc.) is from mid-13c.; the meaning "credit upon the grounds of authority or testimony without complete demonstration, accept as true" is from early 14c. The general sense of "be of the opinion, think" is from c. 1300. Related: Believed (formerly occasionally beleft); believing.

The form beleeve was common till 17c., the spelling then changed, perhaps by influence of relieve, etc. To believe on instead of in was more common in 16c. but now is a peculiarity of theology; believe of also sometimes was used in 17c. The expression believe it or not is attested by 1874; Robert Ripley's newspaper cartoon of the same name is from 1918. Emphatic you better believe attested from 1854.