Since I had no luck in finding a definition for the figurative meaning of thick end of the wedge (not on the Web nor in any of the word and phrase dictionaries I checked), I used my vast powers of deductive reasoning. I figured if there was a ‘thick end of the wedge’ there might well be a thin end of the wedge. And sure enough it was so, with its definition appearing in several dictionaries.<2012 “This business with Billy rather floored me, and I think—if you don’t mind my saying—I think it’s the thick end of the wedge.”—Elegy for Eddie by Jacqueline Winspear, page 294>[[1933 London and environs. While conducting an investigation, Billy was attacked and beat up.]]
With the ‘thin end’ definition in hand, it seemed that inferring the ‘thick end’ definition would be a breeze. It should be noted that it wasn't possible for me to determine the number of Google hits for the two phrases, since those numbers were mixed in with the hits for the literal meaning. But, as expected, it did appear that the use of‘thin end’ was much more popular than ‘thick end.’
THE THIN END OF THE WEDGE informal (mostly British, Australian, and South African) : An action or procedure of little importance in itself, but which is likely to lead to more serious (and usually unwelcome) developments; a small beginning which it is hoped or feared may lead to something greater; the start of a harmful development. <There are those who see the closure of the hospital as the thin end of the wedge.>
Etymology: The image is of a wedge being driven into a space and doing its work as the thicker part penetrates.)
(Oxford English Dictionary, Oxford Dictionary of Idioms, Allen’s English Phrases, and Cambridge Idioms Dictionary)
The following quotes for ‘thin end of the wedge’ are from the Oxford English Dictionary and archived sources:
__________________________<1856 “Beware, Englishmen, of the tendencies to hierarchy in your country when the thin end of the wedge is introduced: it will work its way on to all this.”—Memories of Old Friends (1882) Journal of C. Fox, xxii. Page 308>
<1896 “How many reforms have the Tories resisted with the thin-end-of-the-wedge argument.”—Daily News (London), 21 February, page 5/1>
<1957 “One member described it as the ‘thin edge of the wedge’ in a attempt to by-pass the committee.”—Sydney Morning Herald (Australia), 16 April, page 1>
<1989 “[He] argued that a court exemption for peyote use would be ‘the thin end of the wedge’ for other groups to petition for exemption of other drugs, such as marijuana, from criminal laws.”—Washington Post (D.C.), 7 November>
<2002 “Gibraltarians see any notion of sharing sovereignty as the thin end of the wedge. The Independent (London), 25 April>
<2008 “Yes, the registration fee has increased in the Budget but we are worried that this is just the thin end of the wedge.”—Daily Mail (London), 25 October>
<2013 “The group says it is concerned about ‘the pillage of the countryside’. And it fears the plan could be the thin end of the wedge for more homes later.”—North Devon Journal (U.K.), 8 August>
Now I should be able to deduce the answer to my question. The ‘thick end of the wedge’ means …. means . . . (>:)
THICK END OF THE WEDGE: ??? [[To be determined]]
Well, while I flounder around, Wordwizards from across the sea are probably laughing up their sleeves that this expression would be causing me a problem.
New plan of attack –The following are some quotes from archived sources that I’ll use to try to come up with a definition:
The following are some definition guesses:<1879 “The reduction in the value of improvements was an act of repudiation. . . If they conceded this, the thick end of the wedge would be inserted for the further act of repudiation – that of abolishing the interest.”—The Sydney Morning Herald, 11December, page 2>
<1930 “Lord Irwin, the Viceroy asked Gandhi which point he would like discussed first. Gandhi then struck in with the thick end of the wedge and said that the important point was whether any conference called by the government would have power to deal with the question of dominion status.”—Charleston Gazette (West Virginia), 14 may, page 6>
<1967 “. . . ‘anticolonialism’ swept Great Britain at war’s end from every valuable overseas position she had ever known, and drove her back upon and island never meant to be self-supporting. This was the thick end of the wedge; and once it was driven in, de Gaulle of France set out happily to finish the job. He hated England . . . ever since the blackest days of the war.”—The News-Dispatch (Jeannette, Pennsylvania ), 27 November>
<1994 “The magistrate, . . . last week sentenced 16 culprits . . . The 16 all belonged to a now-dissolved police intelligence unit . . . whose activities made it, the judge ruled, ‘an illicit terrorist organization.’ Senior police officers see this as the thick end of the wedge. They are to be made the scapegoats, they feel, for all the murders, tortures and beatings committed during the 17 years of military rule.”—The Economist (U.S.), 9 April> 
<2001 “If the world at any level accepted the threat of climate change in 1991, Earth Summit year, then the thick end of the wedge in the years ahead could, in principle, be thick indeed.”—The Carbon War: Global Warming and the End of the Oil Era by J. K. Leggett, page 95>
<2008 “Turning off the power to a house with a ventilator was the thick end of the wedge in a period which has seen power leap in cost.”—Marlborough Express (Wellington, New Zealand), 24 September> [[Women on ventilator died when power to her house was shut off for missing a rent payment ]]
<2012 “However, when it comes to risk-transfer, the private sector is seen to be getting the thick-end of the wedge.”—The Australian (Surry Hills, New South Wales), 17 April>
<2013 “UK should stay clear of Syria: . . . All military intervention in huge, messy conflicts is essentially open-ended, and must be: this is not a dalliance we should start without examining the potentially thick end of the wedge.”—The Times (London), 24 June>
THE THICK END OF THE WEDGE: The stronger side of something; the objectionable/bad/difficult/down side of something; the bad end of the bargain; the shitty end of the stick; a raw deal.
With regard to the original quote (top of page), I would say that there it means ‘the down side of something.’ Three years ago Billy had become the assistant to a private investigator, had encountered no serious difficulties, and had been enjoying his job. With this attack, he encountered for the first time the down side of his work.
And now if someone in the know would tell me what they take thick end of the wedge to mean, it would be greatly appreciated.
Ken G – August 14, 2013