How did the expression "put the blame on" come about?

Christine Ammer, The American Heritage Dictionary of Idioms (1997) has discusses "put the blame on" in two separate entries—for "lay on" and for "put it to":

lay on ... 3. Impose or cast something on someone, as in The government laid a tax on landholders, or Dad had a way of laying the guilt for his shortcomings on his partners. This usage is also found in lay or put the blame on someone, as in Nancy could always find someone to lay the blame on, or Jerry put the blame on Bill. {1300s}

...

put it to ... 3. Overburden with tasks or work, as in They really put it to him, expecting [him] to do all the packing. 4. Blame on, as in They didn't know who broke the window so they put it to Sam.

A Google Books search finds an instance of "put the blame" that purportedly dates to 1566—although the phrase in this instance attaches to the preposition to, not on. From "A Relation of the Death of David Rizzi, Chief Favorite to Mary Stuart Queen of Scotland, Who Was KIlled in the Apartment of the Said Queen on the 9th of March 1565, Written by the Lord Ruthen, One of the Principal Persons Concerned in That Action" (1566), published in an edition of 1699, and included in Tracts Illustrative of the Traditionary and Historical Antiquities of Scotland, volume 1 (1836):

The said lord caused George to go to wake the king; and after that he had gone in twice o thrice, finding him sleeping so sound, he would not awaken him. Thereat the said lord [Ruthen] was very miscontented; the king slept still till six in the morning, that the Lord Ruthen came and reproved him, that he had not kept his promise to the queen's majesty, in lying with her all that night. His answer was that he was fallen on such a dead sleep that he could not awaken; and put the blame to William Tellor one of of his servants that permitted him to sleep. But always, said he, I will take my night-gown and go up to the queen.

Another fairly early instance occurs in a Parliamentary debate of May 5, 1679, regarding the pardon of the Earl of Danby, in Debates of the House of Commons, From the Year 1667 to the Year 1694, volume 7 (1763):

Serjeant Maynard.} The Earl of Danby has both wronged the King and this House; he has put in a Protestation; which, in effect, is a justification of himself, and a diversion of his crime upon the King. He has charged it on the King, and it was unnecessary for him to do it—But to come and tell a story, upon which no issue can be taken, is but a flourish, and no Plea at all. For putting the blame thus upon the King, he deserves as much punishment as he can do.

And again in Byron's Don Juan (1820), although this is an instance in which the word choice may have been influenced by the opportunity to achieve a desired rhyme:

Haidee and Juan were not married, but

The fault was theirs, not mine: it is not fair,

Chaste reader, then, in any way to put

The blame on me, unless you wish they were;

Then if you'd have them wedded, pleas to shut

The book which treats of this erroneous pair;

Before the consequences grow too awful;

'Tis dangerous to read of loves unlawful.

Here (at last) the familiar "put the blame on" phrasing that remains in use today is in effect.

The Ngram chart for "lay the blame" (blue line) versus "put the blame" (red line) versus "place the blame" (green line) for the period 1770–2005 indicates that "lay the blame" was the most common form in published writing until the 1940s, when "put the blame" seems to have overtaken it:

Today the frequencies of all three forms appear to be very similar. I haven't been able to discover any particular trigger that led to the surge in popularity of both "put the blame" and "place the blame" during the 50-year period from 1890 to 1940, but that's a long stretch of time and the progress looks fairly gradual on the chart, so it may represent an organic, incremental change in usage rather than one triggered by a particular notorious or otherwise influential instance of use.

The phrase "put the blame" goes back many years, and the mystery is as much that it persisted for so long in relative obscurity in published English (compared with "lay the blame") as that it finally achieved popular predominance after so long a period of relative disuse.