“peruse quickly” (to skim)
presented to him, to peruse quickly the embossed page, and to acquire correct ideas from the objects with which he is brought in contact. (1893)
obviously one cannot study every page in much detail. The theological and literary works I can peruse quickly enough, since ... (1933)
One has only to peruse quickly the history of ideas of the last few decades and look even superficially at current life the world over to feel convinced that secularism ... (1949)
Let me say, Mr Chairman, that I had an opportunity to peruse quickly the report that came from Gen. Carl R. Grav on this matter ... (1963)
The folders that you received have in them books which we sincerely hope you will peruse quickly and that you will make your exchanges as rapidly as possible, in order to assist the Committee. (1966)
As such it will ease oceanographers' work load by allowing the scientists to peruse quickly all available data on the ocean's physical nature (1970)
I have had an opportunity to peruse quickly through your testimony. I notice it is a long statement. You, of course, can read it if you desire. (1972)
Like Aldo Leopold works, the art of photographer Les Blacklock is not something to peruse quickly. (1974)
Consequently, lengthy climbing tales can slow those trying to peruse quickly. But several users said such stories attract them to rec.climbing. (1995)
If a judge has not read the entire brief prior to oral argument, the Summary of Argument is a valuable substitute which the judge can peruse quickly prior to the hearing (1996)
And for that reason, if the reader of this second half of the study wants to peruse quickly the most salient part of the preceding for a background, I recommend therein the first chapter's sections on Greek tragedy, ... (2004)
If anyone desires intently to know the content of the whole book let him first peruse quickly these preceding chapter ... (2005)
The chairman, presented with a passage to peruse quickly , refused 'for common decency's sake' to permit it to be read aloud (2006)
This book will be written in plain language, often in point form because my objective for doing this is to make it easy for parents and other interested persons to peruse quickly (2009)
Bart and Mark had drawn on their experience and training as trial lawyers to organize their notes into snippets that Christa could peruse quickly. She employed her speed-reading skills to absorb the dominant points that her assistants had ... (2011)
There were some documents dealing with real estate holdings and, from what she could peruse quickly, documents and letters from other businesses and enterprises ... (2012)
Source: Google Books
These results exclude instances where a noun is between the verb and its adverb such as: to peruse the manual quickly, or peruse the reports quickly. It also excludes instances when the pronoun it and other adverbs are employed such as: I picked it up to peruse it real quick. Nevertheless. these examples prove without doubt that native speakers use peruse to mean “to skim” or “to glance through”.
The OP asks why the more recent definition of peruse has made its way to the top of Merriam-Webster's entry. The answer is to be found in Merriam-Webster's own website
How does a word get into a Merriam-Webster dictionary?
[emphasis mine]
This is one of the questions Merriam-Webster editors are most often
asked.
The answer is simple: usage.
Tracking Word Usage
To decide which words to include in the dictionary
and to determine what they mean, Merriam-Webster editors study the
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a cross section of published material, including books, newspapers,
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called "reading and marking." The editors scour the texts in search of
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inflected forms–in short, anything that might help in deciding if a
word belongs in the dictionary, understanding what it means, and
determining typical usage. Any word of interest is marked, along with
surrounding context that offers insight into its form and use.
[. . .]
Merriam-Webster's citation files, which were begun in the 1880s, now contain 15.7 million examples of words used in context and cover all aspects of the English vocabulary. Citations are also available to editors in a searchable text database (linguists call it a corpus) that includes more than 70 million words drawn from a great variety of sources.
[. . .]
Size Does Matter
The size and type of dictionary also affects how many citations a word
needs to gain admission. Because an abridged dictionary, such as
Merriam-Webster's Collegiate® Dictionary, has fairly limited space,
only the most commonly used words can be entered; to get into that
type of dictionary, a word must be supported by a significant number
of citations. But a large unabridged dictionary, such as Webster's
Third New International Dictionary, has room for many more words, so
terms with fewer citations can still be included.
Authority Without Authoritarianism
Change and variation are as natural in language as they are in other areas of human life and Merriam-Webster reference works must reflect that fact. By relying on citational evidence, we hope to keep our publications grounded in the details of current usage so they can calmly and dispassionately offer information about modern English. That way, our references can speak with authority without being authoritarian.