Related:
"Much though" vs "much as",
Use of 'Much as' [closed],
Using “as much as” at start of sentence
Consider the following two variations:
As much as I hate to admit it, I cannot swim.
Much as I hate to admit it, I cannot swim.
Both seem to be standard, as they both enjoy wide use, but based on the answers to the linked questions above, one gets the impression that the latter derives from the former (and that the former is preferred). I find this suspect for a couple of reasons.
First, I have a much easier time parsing the bare "much as" variation because one of the definitions of "as" is precisely a conjunction meaning "though" (#9). Hence, these should be equivalent:
Much as I hate to admit it, I cannot swim.
Much though I hate to admit it, I cannot swim.
Though I much hate to admit it, I cannot swim.
Whereas "as much as" I interpret as idiomatic.
Secondly, the bare "much as" seems to be closely related to other concessive expressions that strictly preclude any initial "as":
But, fool as he is, I won't have him drowned.
Try as we may, none of us can be free of conflict and woe.
Very much as I hate to admit it, I cannot swim.
The last one I made up, but I can't see why it wouldn't be possible, though admittedly I haven't been able to find it in the wild.
So, all that said, I'm led to believe that "much as" is the original expression, but am not sure how to verify it apart from asking you all.
Best Answer
To investigate this question via Google Books, I ran searches for a small subset of potential matches: "but as much as," "but much as," "and as much as" and "and much as." My goal was simply to look at what these "core samples" (to use a geological term) turned up, and to see whether the results supported any larger inferences about the relative age of the concessive "as much as" versus the concessive "much as."
The earliest match for a concessive "but as much as" in a Google Books search appears in Edward Stillingfleet, Origines Britannicae, or The Antiquities of the British Churches (1685):
The next-earliest match is in Peter Pett, The Happy Future State of England (1688):
A couple of fairly early instances come from very prominent authors. From Richard Steele, The Tatler, No. 48 (July 30, 1709):
From Daniel Defoe, The Fortunate Mistress (1724):
The first match for a concessive "but much as" in the Google Books search results is from "Summary of Proceedings in the present Session of Parliament, Thursday, Feb. 17," in The Gentlemen's Magazine and Historical Chronicle (April 1785):
The phrase "and as much as" used concessively first appears in a Google Books match from William Sherlock, "A Sermon Preach'd at St. Paul's Cathedral, November 22, 1699" (1699):
Three years later, from Charles Trimnell, "An Answer to a Third Letter to a Clergyman in the Country, in Defence of the Entry of the Parliament-Writ, &c." (1702), we have this:
The first match for a concessive "and much as" in the Google Books search is from "The Tears of Cambria" (1773):
The first prose example of "and much as" appears in the Google Books search results appears in "Summary of Proceedings in the present Session of Parliament, Tuesday, Jan. 3," in The Gentleman's Magazine (February 1786):
To sum up, my Google Books searches for concessive "but as much as" and "and as much as" yielded matches from the late 1600s forward. The corresponding Google Books searches for concessive "but much as" and "and much as" turned up valid matches in prose beginning in 1785 and 1786, respectively—both, coincidentally, from reports of Parliamentary debates—with one earlier poetic occurrence from 1773.
Since my sample is narrowly defined, I can't draw any definitive conclusions, but the search results I obtained certainly suggest that concessive use of "as much as" is considerably older than concessive use of "much as."