When the constituent structure of a word or phrase fades over time, i. e., when the meaning and resultant separability of the constituents cease to be transparent to the speakers of a language, the word or phrase may be conflated with another one, whose meaning is similar, leading to variants that are not on a par orthoepically. This is what has happened with the phrase on behalf of in the recent history of (American) English.

More and more in public discourse, instead of on the part of in its strictly instrumental (agentive) meaning speakers substitute on behalf of, whose traditional meaning is ‘for the benefit of; in the interest of’ rather than ‘as the agent of; on the part of’. The American Heritage Dictionary of the English Language (4th ed., 2006) records this substitution and (typically) makes no distinction in its Usage Note:

Usage Note: A traditional rule holds that in behalf of and on behalf of have distinct meanings. In behalf of means “for the benefit of,” as in We raised money in behalf of the earthquake victims. On behalf of means “as the agent of, on the part of,” as in The guardian signed the contract on behalf of the minor child. The two meanings are quite close, however, and the phrases are often used interchangeably, even by reputable writers.

But as the etymological data in the Oxford English Dictionary Online entry give one to understand, the present-day ascription of purely instrumental meaning to on behalf of, by which this phrase is equated with on the part of, is a misconstrual of its structure. Here are the two relevant etymologies, for half and behalf:

Etymology: A Common Germanic n.: Old English healf (feminine) = Old Saxon halƀa (Middle Dutch, Middle Low German halve ), Old High German halba (Middle High German halbe ), Old Norse halfa (hálfa), Gothic halba side, half . . .The oldest sense in all the languages is ‘side’.

Etymology: Used only in the phrases on, in behalf (of), in, on (his, etc.) behalf , which arose about 1300, by the blending of the two earlier constructions on his halve and bihalve him, both meaning ‘by or on his side’ . . . By the mixture of these in the construction on his bihalve, . . . previously a preposition, and originally a phrase, be healfe ‘by (the) side,’ became treated, so far as construction goes, as a n., and had even a plural behalfes , behalfs in 16–17th cent. The final -e of Middle English was the dative ending. In modern use, construed either with a possessive pronoun (in my behalf), a possessive case (in the king’s behalf), or with of (in behalf of the starving population); the choice being determined by considerations of euphony and perspicuity. Formerly of was sometimes omitted.

The explanation for the misconstrual and resulting conflation of the two phrases is to be sought in the opacity of the word behalf, which has no currency outside of the two idiomatic phrases noted.