Q Was the Weimar Republic referred to as such by contemporaries?
Yes. Some people at the time sometimes surely used this term.
It probably was not that much in common place popular parlance and surely not anywhere used as anything 'official'.
But in terms of (sometimes a bit academic) debate, this moniker was well established before 1933.
Wikipedia is just wrong on this:
Die Verbindung mit dem Stadtnamen Weimar wurde zunächst nur im Zusammenhang mit der Verfassung verwendet; erst 1929, zu deren zehnjährigem Jubiläum, sprachen rückwärtsgewandte Konservative, der Nationalsozialist Hitler und auch das Organ der Kommunisten von der Weimarer Republik. 1932 tauchte dieser Ausdruck aber auch in der republiktreuen Vossischen Zeitung auf. Wikipeda.de:WeimarRepublic
And also wrong is the unsourced English version:
The first recorded mention of the term Republik von Weimar (Republic of Weimar) came during a speech delivered by Adolf Hitler at a National Socialist German Worker's Party rally in Munich on 24 February 1929.
Wikipedia:WeimarRepublic
Example from 1926:
Rätselhaft, wie lange die Republikaner diese Tendenz nicht erkannt haben. Jahre waren nötig, um die Erkenntnis durchbrechen zu lassen, dass die Republik nicht bloß ein Staatswesen mit wählbarem statt erblichem Präsidenten ist sondern ein Wert in sich selbst darstellt. Mancher schlimme Geburtsfehler der Weimarer Republik ist nur aus dem Mangel an jeglicher republikanischer Bewegung zu verstehen.
It is puzzling how long republicans have not recognised this tendency. Years were needed to break through the realisation that the republic is not just a state with an electable rather than hereditary president, but is a value in itself. Some serious birth defects of the Weimar Republic can only be understood from the lack of any republican movement.
Carlo Mierendorff: Republik oder Monarchie? Sozialistische Monatshefte, 32(1926), H. 7, Ausg. vom 12.07. 1926, S. [435] - 439
Example from 1928, also non-Hitlerite, not even right-wing, and amusingly speculating about russiagating elections:
'Rußland und die Reichstagswahlen'
[…] Dreieinhalb Millionen deutscher Proletarier hätten trotz des "wilden antikommunistischen Terrors" sich als geschworene Feinde der Weimarer Republik und als Kämpfer für die proletarische Diktatur erklärt.[…]
Russia and the Reichstag elections
[…] Three and a half million German proletarians had declared themselves sworn enemies of the Weimar Republic and fighters for the proletarian dictatorship despite the "wild anti-communist terror".[…]
Titel: Vorwärts Datum: 24.05.1928 Nummer: 242 Jahrgang: 45 // Vorwärts - Morgenausgabe Nr. A124 (link)
Similarly for the phrase "Republik von Weimar":
We see that Graf Ernst zu Reventlow used it already in 1925 in his book "Minister Stresemann als Staatsmann und Anwalt des Weltgewissens"
Or even in Reichstag protocols from 1928.
What seems to be true in both Wikipedia articles is that after Hitlerites 'embracing the term as derogatory' — and more often than not in the shortened allusion form of just "Weimar" and making clear it is to be understood in that way things changed.
To get a sense of when the talk at the time was not just about the constitution – "Weimarer Verfassung" is indeed found very often and very early – the more difficult to ascertain aspect is of course that in addition to sources like the above some people might have used the shorthand "Weimar" and leaving out any construction with "republic", just like most of the Social-democrats went for the shorthand "Republik" most often. Although that would probably be a bit indicative of using that term "Weimar" in a negative light.
But that the term "Weimarer Republik" or "Republik von Weimar" only came into being that late as 1929 as claimed by Wikipedia and then at first only as a conservative or Nazi-right-wing epithet is evidently untrue.
While I don't have a good quality corpus linguistics analysis at the ready to compare the actual popularity for that term versus alternative phrases or even compared to official designations, (like "Das Reich", "Deutsches Reich", "die deutsche Republik", "die Republik" or "unser Land" etc.) we cannot rely on either 'Wikipedia info' or horribly OCR'd google-books from a fraction of what we actually have as plentiful sources for the time.