Greetings! This is one of those "hidden gem" questions about the various border changes from the Treaty of Versailles, and it certainly seems (at least on the surface), that the simple fact of the matter is that the Allied delegation just "gave" Eupen-Malmedy to Belgium with no particular reasoning whatsoever. For more information however, on why Belgium did not recieve more in addition to Eupen-Malmedy (as there certainly were other regions which might have been logically given to the Belgians), see this thread I weighed in on. With that preamble out of the way, let us begin.

Note: Due to the rather obscure nature of the topic, many of the sources used for this response are rather old, but they do give us a good glimpse/overview of the Eupen-Malmedy question nonetheless.

Going further back into the history of these provinces (or kreise, to use the German term for these "districts"), there does seem to be some sort of a historical argument for the return of these provinces to Belgium. Prussia only came into possession of the provinces in 1814-1815, as compensation for its renouncement of claims to Saxony. Further, the Belgians could (and did) allege with some basis that the vast majority of both Eupen and Malmedy had been part of the modern Kingdom of Belgium ever since its founding, and that the German counter-claim, which relied on the provinces being included within vaguely drawn Circles on a map from the Holy Roman Empire (dated 1512), was a bit shaky.

There was also the military consideration for the Allied delegation. In Malmedy, the German mobilization camp of Elsenborn had enabled the German Empire's war machine to kick into high gear far more quickly. It had been from Elsenborn that troops assembled as part of General Otto von Emmich's Army of the Meuse. These troops were tasked with securing the forts of Liege and the invasion roads for the rest of the army. To deprive Germany of this mobilisation point, which might otherwise have been used to launch another campaign on the Low Countries and France in the future, was a key aim of the Allies. The district of Malmedy was also far more akin to the Belgian provinces to the west of it rather than the German ones to the east, owing in part to its largely agricultural economics, and the fact that there was a considerably Walloon element in its populace (Prussian statistics revealed an estimated 9,500 Walloons within the entire Kreis, out of a total population of 34,768 in 1910). Interestingly, for these various reasons, the Belgian government had actually received petitions from the populace of Malmedy asking for annexation.

What about Eupen then? Here the argument for ethnic and economic reasons was less strong. The province contained practically no Walloons and was closer to the German industrial hub of Aachen. There were no major mobilisation hubs within the Kreis, and the historical case was not as strong as it had been for Malmedy.

What the Allied diplomats at Versailles actually responded to the Germans' "Remarks" protesting this handover of Eupen were the following:

• The zinc mines in the Kreis were of key economic importance to the district, and could be used by the Belgians in their efforts to rebuild a ruined postwar industry,
• The vast timber resources situated within Eupen could also be used to rebuild devastated Belgian towns and infrastructure, whereas Belgian lumber in other districts had been used up by the German forces during their occupation,
• Finally, Belgian control of the headwaters of the Vesdre rivers would be of advantage to their operation of the canal system in Eastern Belgium.

Remember however, that the Allied delegation took pains to emphasise that these reasons "justif[ied] the reunion of the territory to Belgium provided [sic] the petitions to this effect are sufficiently supported by the population of the district." The "petitions" they referred to were outlined in Article 34 of Part II of the Versailles Treaty:

Article 34: Germany renounces in favour of Belgium all rights arid title over the territory comprising the whole of the Kreise of Eupen and of Malmedy. During the six months after the coming into force of this Treaty, registers will be opened by the Belgian authority at Eupen and Malmedy in which the inhabitants of the above territory will be entitled to record in writing a desire to see the whole or part of it remain under German sovereignty. The results of this public expression of opinion will be communicated by the Belgian Government to the League of Nations, and Belgium undertakes to accept the decision of the League

When the registers closed on the 23rd of July 1920, only 271 names out of a total of 33,678 potential persons were recorded. Rather amusingly, 202 of those names were the signatures of former German officials, whilst the remaining 69 were actual citizens of Eupen-Malmedy (for further breakdown, only 62 signatures were from Malmedy, whilst 209 were from Eupen).

So there we have it then: the various economic, military, historical, and ethnic reasons for the handover of Eupen-Malmedy to Belgium in the Treaty of Versailles. Hope you found this response helpful, and feel free to ask any follow-ups as you see fit!

Sources

George, Robert H. "Eupen and Malmedy." Foreign Affairs 5, no. 2 (1927): 332-35. Accessed March 7, 2021. https://www.jstor.org/stable/20028533.

Grathwol, Robert P. "Germany and the Eupen-Malmédy Affair 1924-26: "Here Lies the Spirit of Locarno"." Central European History 8, no. 3 (1975): 221-50. Accessed March 7, 2021. http://www.jstor.org/stable/4545745.

A. R. H. "The Belgian-German Boundary Demarcation." The Geographical Journal 57, no. 1 (1921): 43-51. Accessed March 7, 2021. https://www.jstor.org/stable/1781205.