The prefix shift to af- took place 16c. under mistaken belief that it was a Latin word in ad-; change of -th- to -d- took place late 16c. (and also transformed burthen, spither, murther, etc. into their modern forms).
The notion of "accomplish" (late Old English) gradually became "be able to bear the expense of, have enough money" to do something (late 14c.), and the original senses became obsolete. Of things, "be capable of yielding," 1580s, which is the sense in afford (one) an opportunity. Related: Afforded; affording.
"a load, that which is borne or carried," Old English byrðen "a load, weight, charge, duty;" also "a child;" from Proto-Germanic *burthinjo- "that which is borne" (source also of Old Norse byrðr, Old Saxon burthinnia, German bürde, Gothic baurþei), from PIE root *bher- (1) "to carry," also "to bear children."
The shift from -th- to -d- began early 12c. (compare murder (n.), rudder, afford). Archaic burthen is occasionally retained for the specific sense of "capacity of a ship." Beast of burden is from 1740. Burden of proof (Latin onus probandi) "obligation on one party in an action to establish an alleged fact by proof" is recorded from 1590s.
Middle English anelen, from Old English onælan "to set on fire, kindle; inspire, incite," from on- "on" (see an- (1)) + ælan "to burn, bake," from Proto-Germanic *ailan, "probably" [Watkins] from the same PIE root meaning "to burn" that is the source of ash (n.1). It is related to Old English æled "fire, firebrand," Old Norse eldr, Danish ild "fire."
The -n- was doubled after c. 1600 by analogy of Latinate words (annex, etc.; compare accursed, afford, allay). Meaning "to treat by heating and gradually cooling" (of glass, earthenware, metals, etc., to toughen them) was in late Old English. Related: Annealed; annealing.
word-forming element expressing direction toward or in addition to, from Latin ad "to, toward" in space or time; "with regard to, in relation to," as a prefix, sometimes merely emphatic, from PIE root *ad- "to, near, at."
Simplified to a- before sc-, sp- and st-; modified to ac- before many consonants and then re-spelled af-, ag-, al-, etc., in conformity with the following consonant (as in affection, aggression). Also compare ap- (1).
In Old French, reduced to a- in all cases (an evolution already underway in Merovingian Latin), but written forms in French were refashioned after Latin in 14c. and English did likewise 15c. in words it had picked up from Old French. In many cases pronunciation followed the shift. Over-correction at the end of the Middle Ages in French and then English "restored" the -d- or a doubled consonant to some words that never had it (accursed, afford). The process went further in England than in France, where the vernacular sometimes resisted the pedantic, resulting in English adjourn, advance, address, advertisement (Modern French ajourner, avancer, adresser, avertissement). In modern word-formation sometimes ad- and ab- are regarded as opposites, but this was not in classical Latin.
Proto-Indo-European root forming prepositions, etc., meaning "forward," and, by extension, "in front of, before, first, chief, toward, near, against," etc.
It forms all or part of: afford; approach; appropriate; approve; approximate; barbican; before; deprive; expropriate; far; first; for; for-; fore; fore-; forefather; foremost; former (adj.); forth; frame; frau; fret; Freya; fro; froward; from; furnish; furniture; further; galore; hysteron-proteron; impervious; improbity; impromptu; improve; palfrey; par (prep.); para- (1) "alongside, beyond; altered; contrary; irregular, abnormal;" paradise; pardon; paramount; paramour; parvenu; pellucid; per; per-; percent; percussion; perennial; perestroika; perfect; perfidy; perform; perfume; perfunctory; perhaps; peri-; perish; perjury; permanent; permeate; permit; pernicious; perpendicular; perpetual; perplex; persecute; persevere; perspective; perspire; persuasion; pertain; peruse; pervade; pervert; pierce; portray; postprandial; prae-; Prakrit; pre-; premier; presbyter; Presbyterian; preterite; pride; priest; primal; primary; primate; primavera; prime; primeval; primitive; primo; primogenitor; primogeniture; primordial; primus; prince; principal; principle; prior; pristine; private; privilege; privy; pro (n.2) "a consideration or argument in favor;" pro-; probably; probe; probity; problem; proceed; proclaim; prodigal; produce; profane; profess; profile; profit; profound; profuse; project; promise; prompt; prone; proof; proper; property; propinquity; prophet; prose; prostate; prosthesis; protagonist; Protean; protect; protein; Proterozoic; protest; proto-; protocol; proton; protoplasm; Protozoa; proud; prove; proverb; provide; provoke; prow; prowess; proximate; Purana; purchase; purdah; reciprocal; rapprochement; reproach; reprove; veneer.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pari "around, about, through," parah "farther, remote, ulterior," pura "formerly, before," pra- "before, forward, forth;" Avestan pairi- "around," paro "before;" Hittite para "outside of," Greek peri "around, about, near, beyond," pera "across, beyond," paros "before," para "from beside, beyond," pro "before;" Latin pro "before, for, on behalf of, instead of," porro "forward," prae "before," per "through;" Old Church Slavonic pra-dedu "great-grandfather;" Russian pere- "through;" Lithuanian per "through;" Old Irish ire "farther," roar "enough;" Gothic faura "before," Old English fore (prep.) "before, in front of," (adv.) "before, previously," fram "forward, from," feor "to a great distance, long ago;" German vor "before, in front of;" Old Irish air- Gothic fair-, German ver-, Old English fer-, intensive prefixes.
1590s, transitive, "afford refuge;" 1630s, intransitive, "take refuge, seek shelter or protection," from refuge (n.) or (adj.). Marked "now rare" in OED; take refuge being the more usual verb form. Related: Refuged; refuging.