mid-14c., deifien, "to make god-like;" late 14c., "make a god of, exalt to the rank of a deity," from Old French deifier (13c.), from Late Latin deificare, from deificus "making godlike," from Latin deus "god" (from PIE root *dyeu- "to shine," in derivatives "sky, heaven, god") + -ficare, combining form of facere "to make, do" (from PIE root *dhe- "to set, put"). Sense of "adore, regard as an object worthy of worship" is from 1580s. Related: Deified; deifying.
Old English pyffan, *puffian "to blow with the mouth," of imitative origin. Compare pouf, from French. Especially "to blow with quick, intermittent blasts" (early 14c.). Meaning "pant, breathe hard and fast" is from late 14c.
The meaning "to fill, inflate, or expand with breath or air" is by 1530s. The intransitive sense, in reference to small swellings and round protuberances, is by 1725. The transitive figurative sense of "exalt" is from 1530s; shading by early 18c. into the meaning "praise with self-interest, give undue or servile praise to." Related: Puffed; puffing.
late 13c., anhaunsen "to raise, make higher," from Anglo-French enhauncer, probably from Old French enhaucier "make greater, make higher or louder; fatten, foster; raise in esteem," from Vulgar Latin *inaltiare, from Late Latin inaltare "raise, exalt," from altare "make high," from altus "high," literally "grown tall" (from PIE root *al- (2) "to grow, nourish"). The meaning "raise in station, wealth, or fame" attested in English from c. 1300. Related: Enhanced; enhancing.
The -h- in Old French supposedly is from influence of Frankish *hoh "high." The -n- perhaps is due to association with Provençal enansar, enanzar "promote, further," from enant "before, rather," from Latin in + ante "before."
Cognates include Greek talantos "bearing, suffering," tolman "to carry, bear," telamon "broad strap for bearing something," talenton "a balance, pair of scales," Atlas "the 'Bearer' of Heaven;" Lithuanian tiltas "bridge;" Sanskrit tula "balance," tulayati "lifts up, weighs;" Latin tolerare "to bear, support," perhaps also latus "borne;" Old English þolian "to endure;" Armenian tolum "I allow." Figurative sense of "praise highly" in English is first attested c. 1500. Related: Extolled; extolling.
Related to have (Old English habban "to hold, possess"). Meaning "to throw" is from 1590s. Nautical meaning "haul or pull" in any direction is from 1620s. Intransitive use from early 14c. as "be raised or forced up;" 1610s as "rise and fall with alternate motion." Sense of "retch, make an effort to vomit" is first attested c. 1600. Related: Heaved; heaving. Nautical heave-ho was a chant in lifting (c. 1300, hevelow).
Intransitive sense of "to rise, to seem to rise" (of clouds, fogs, etc.) is from 1834. Figurative sense of "to encourage" (with up) is mid-15c. The meaning "steal, take up dishonestly" (as in shoplift) is 1520s. Surgical sense of "to raise" (a person's face) is from 1921. Middle English also had a verb liften (c. 1400). Related: Lifted; lifting.