"Thus" vs. "Thusly"

Merriam-Webster's Eleventh Collegiate Dictionary (2003) has entries for thus and thusly, and does not indicate that the latter is colloquial or otherwise inappropriate for everyday use. Here are MW's entries for the two words:

thus adv [ME fr. OE; akin to to OS thus thus] (bef. 12c) 1 : in this or that manner or way {described it thus} 2 : to this degree or extent : SO {thus far} 3 : because of this or that : HENCE, CONSEQUENTLY 4 : as an example

thusly adv (1865) : in this manner : THUS

These definitions raise several points. First, thus is clearly a much older word than thusly. Second, thusly doesn't have any meanings beyond those covered by thus. And third, thusly may have a narrower meaning than thus, although the MW definition isn't terribly illuminating on this point.

With regard to the third point, the only definition attached to thusly ("in this manner") matches the first definition of thus ("in this or that manner or way") quite neatly, so we might suppose that thusly does not generally mean any of the other three things that the dictionary says thus can mean. And indeed the vast majority of instances of thusly that I can recall seeing occur in the context of sentences such as this one, from Henry Little, A History of the Black Hawk War of 1832, third revised edition (1875), reprinted in Michigan Historical Collections, volume 5 (1884):

Gem being in the company of so many men who were hurrying about here and there, to find their places in the ranks, in the confusion and excitement, became much confused in regard to his own identity, and began to reason with himself thusly: ...

However, in some instances the second definition of thus ("to this degree or extent: SO") seems to be closest to the author's intention, as in this example from Transactions of the Grand Lodge of Free and Accepted Masons of the State of Michigan (1887):

Now, Brother Sayre, refer to page 235 of your proceedings, and tell me why my residence is made to read Detroit; why is it thusly? Change it at once to our lovely valley city, Grand Rapids—not that I love Detroit less but Grand Rapids more.

Instances in which thusly appears to have the meaning of the third definition of thus ("because of this or that : HENCE, CONSEQUENTLY")—as appears to be the case in the OP's example—are even more rare, at least in Google Books search results. But evidently they do occur in real life, which may explain why the MW definition of thusly, after seeming to limit its observed and approved use to thus definition 1, ends by equating it with THUS in general.

Many authorities have condemned any use of thusly as a needless alteration of thus. For example, John Lewis Haney, Good English: A Practical Manual of Correct Speaking and Writing (1917): has this to say about thusly:

thusly. Thusly should not be used for thus, as in "Were I in your place, I should act thusly." The word should be reserved for our humorists.

(The American humorist Artemus Ward was famous for asking "Why is this thusly?")

More-recent commenters have continued to express hostility toward thusly. One particularly strident criticism occurs in Robert Hartwell Fiske's Dictionary of Unendurable English (2011), a volume that has much of the flavor of one of the classic prescriptivist works of the 1800s and early 1900s:

thusly Misused for thus. • Because this was described as school shootings and thusly presented as gender neutral, the gendered nature of the killing and shooting was ignored. USE thus. • Thusly the Pagans treat their Idols, and thusly most Christians treat their Bible. USE thus. • It is impossible not to like a movie in which Elizabeth Hurley is cast as Satan, and she is thusly cast in Bedazzled, about which there is considerable buzz, as they say. USE thus. • So, if we were being as literal as it is possible to be, we would construe Mr. Davies's passage thusly. USE thus.

Thusly, like the equally silly muchly, is a substandard word. Thus is the adverb.

Bryan Garner, Garner's Modern American Usage, third edition (2009) agrees in spirit if not in tone with Fiske:

Thusly. Thus itself being an adverb, it needs no -ly. Although the NONWORD *thusly has appeared in otherwise respectable writing, it remains a serious lapse—e.g.: • “Jackson, a counterpuncher by nature, responded thusly [read thus] yesterday to such thoughts: ..." Ron Borges, "Jackson Has a Rallying Cry vs. Lewis: 'No Surrender,'" Boston Globe, 5 May 1994, at 79.

And yet, to judge from this Ngram chart for the period 1800–2000, thusly was considerably more frequent in twentieth-century publications than it had been in nineteenth-century ones:

Evidently, thusly rubs a lot of people (or a few loud people) the wrong way, which is a valid point to consider when deciding whether to use it. But it also appears to be in widespread use, particularly in the sense of "in this manner or way," and it poses no risk of being misinterpreted as meaning something other than what its author has in mind. Under the circumstances, I think objections to thusly amount to points of nicety rather than implicating issues of coherence or clarity.

One might similarly argue that secondly and thirdly are unnecessary in view of the fact that the shorter alternatives second and third can be used adverbially; but far fewer critics condemn secondly and thirdly, maybe because second and third are also adjectives, thus providing cover for secondly and thirdly as uniquely adverbial forms. A nonword that has been around for 150 years begins to look a lot like a word. Maybe it's time to let writers use thusly in peace.

Thusly is simply the adverb form of thus. If an adverb should be used, use the adverb form thusly.

Other answers have aimed at the redundancy of thusly, but I want to highlight its usefulness.

Thus has two senses: "as a result or consequence of this; therefore" and "in the manner now being indicated or exemplified; in this way". But thusly can only be used in the second sense. Thus thusly is useful when the writer wants to avoid confusion between the two senses of thus.

For example:

Because the treatment was said to be efficacious, and thus reported by the national press, many were persuaded to try it.

Was it reported by the press because it was said to be efficacious, or was it reported as efficacious?

Certainly there are other ways to disambiguate the meaning (we could say "reported as such", etc.) but thusly is so economical. Why should it not be used?

Etymonline says it very clearly, thus is an adverb, meaning in this way, from an old case form belonging to this and that. Adding an adverb ending to thus is superfluous. Nevertheless thusly can be found, often humorously, but as Etymonline says it is frowned upon.

Ngram thus, thusly