"to split," O.E. cleofan "to split, separate" (class II strong verb, past tense cleaf, past participle clofen), from P.Gmc. *kleubanan, from PIE base *gleubh- "to cut, slice." Past tense form clave is recorded in Northern writers from 14c. and was used with both verbs (see cleave (2)), apparently by analogy with other ME strong verbs. Common to c.1600 and still alive at the time of the King James Bible; weak p.t. cleaved also emerged in 14c. for this verb; cleft is still later. The p.p. cloven survives, though mostly in compounds.
"to adhere," O.E. clifian, from W.Gmc. *klibajanan, from PIE *gloi- "to stick." The confusion was less in O.E. when cleave (1) was a class 2 strong verb and cleave (2) a class 1 verb; but it has grown since cleave (1) weakened, which may be why both are largely superseded by stick and split.