Long-time lurker, first-time poster. Mods, please let me know if my response is in any regard not up to snuff. I'm happy to go back and provide specific end/footnotes if that's required.

One important consideration I'd like to make before responding to the question is its vast scope. Aristotle was an incredibly prolific writer, and wrote works in fields spanning zoology, ethics, and political philosophy. Likewise, the precise nature of, and reasons for, Aristotle's influence can clearly vary from field to field.

I'd like to take the time to comment specifically on Aristotle's influence within the field of economics, and to push back somewhat on the notion that early Muslim scholars were "obsessed" with him as is often alleged (one primary example being seminal economist Joseph Schumpeter's History of Economic Analysis, in which he largely dismisses the contributions of Islamic scholars to the field in the centuries between Aristotle and St. Thomas Aquinas). I'll try my best to provide context and explanations wherever possible, while also presenting a cogent answer.

Let's begin with a broad overview of Aristotle's contributions to the economic field. It is true and important to acknowledge that, within the field of economics specifically, Aristotle did make several key contributions that help rank him as one of the foremost of the early proto-economic thinkers (an important note-- "economics" as a field we understand today did not begin to emerge until the end of the Mercantilist era and the eve of, among others, the Classical School and Adam Smith). Aristotle was one of the first thinkers to [correctly] identify money's purpose as being a medium of exchange, a store of value, and a unit of account. This represents the current, conventional view within macroeconomics as to money's purpose, and distinguished him from contemporaries such as Plato (who merely viewed money as a medium of exchange). Moreover, Aristotle also arguably developed a rudimentary understanding of the modern microeconomic concept of the consumer surplus in his view that individual parties take to a given transaction/exchange out of a perceived mutual advantage. Much of Aristotle's thought in this regard can be found in his Nicomachean Ethics.

However, Aristotle's thought was not without its limitations. As pervades much of Ancient Greek thought, Aristotle was keen to draw distinctions based on the "natural" versus the "unnatural", and to make normative prescriptions therein. That is to say, he would make economic prescriptions on the basis of what was or was not perceived as just, and often failed to draw a distinction between the normative (subjective preferences grounded in one's individual values & beliefs) and the positive (empirical, descriptive writings on economic phenomena) as economists do today.

Among his more spurious claims was his disdain for money earned from interest (what he referred to as usury), which he alleged was "most reasonably hated because its gain comes from money itself." Specifically, he believed money to be 'unproductive', and the accumulation of wealth beyond satisfying one's basic needs to be 'unnatural.' The conventional view in economics today, by contrast, is that interest serves a valid and important use in economic exchange, as a means of compensation for consumption foregone on the part of the lender, and the risk assumed in acceding to the terms of a loan. Suffice it to say, Aristotle was an imperfect contributor whose lasting contributions might be accurately received as "mixed".

Now, let us turn to your question-- the idea that early Muslim scholars were "obsessed" with him and/or his writings. If we take this view to be true, we might assume that early Muslim scholars who wrote after him paid an intellectual fealty to him. His ideas should pervade their thinking, be accepted in their own writings, and possibly even be regurgitated in one form or another.

This is largely not true. As evidence to this fact, I'm going to highlight some key diversions early Muslim scholars made from Aristotelian economic thought, as well as show many of their own, original, contributions to the field.

To start, early Muslim scholars had a much more charitable view with regards to their view on wealth accumulation. While the Quran and the Hadith refer to "Riba" (interest) in a negative light, they view both wealth and profit very positively. Production and trade were regarded as noble professions, whereas in Aristotle's ancient Greece they were seen as inferior to military and agriculture. Moreover, while Aristotle's proto-economic contributions are typically constrained to the realm of microeconomic exchange, many early Muslim scholars "demonstrated attempts" at developing their own macroeconomic ideas of "enforcing fiscal and monetary policy, deficit financing, the use of taxation to encourage production, and the existence of credit and credit instruments for the rudiments of checking and savings accounts, banking institutions, and procedures for the formation of partnerships, commendam contracts, and monopolies". They had a demonstrated record of going beyond Aristotle, both in terms of fields of discussion as well as in specific developments within commonly-discussed ideas.

In terms of specific contributors who went well beyond Aristotle, we might look to Abu Yusuf's The Book of Taxation, in which he opposed tax farming, suggested the centralisation of tax administration, and posited something like the four canons of taxation that would go on to be articulated by Adam Smith centuries later. Moreover, various contributors made reference to the concept of division of labor (a concept, to my knowledge, entirely neglected by Aristotle), such as Kai Kavus, Ghazali, and Ibn Miskaway. Hosseini notes that "Although writing before the age of industry, medieval Muslim writers understood the application of division of labor to a productive unit". Kai Kavus is notable for having articulated a sort of rudimentary equivalent to the ideas of supply and demand.

These two preceding paragraphs merely provide a foray into the depth of thought provided by many early Muslim scholars (I'm trying to balance the tension between a substantive answer and getting too into-the-weeds of economic terms that some may not be familiar with), however I think they suffice to show that Muslim scholars, contrary to "obsessing" over Aristotle (and the implications associated with it), developed many original and unique contributions to the field. Now, all of this is not to say that these scholars were not influenced by Aristotle. But I think it is incorrect (at least within the context of Aristotle's economic contributions) to suggest that his thought's influence on these scholars rose to the level of obsessive. I would qualify it as moderate.

I hope this (at least partially) answers your question! My knowledge on the subject is primarily based on a course I took during my undergraduate degree and the readings associated therein.

Sources: Lowry, S. Todd (2009). Ancient and Medieval Economics. In A Companion to the History of Economic Thought (pp. 11–24). Malden, MA.

Hosseini, H. S. (2009). Contributions of Medieval Muslim Scholars to the History of Economics and their Impact: A Refutation of the Schumpeterian Great Gap. In A Companion to the History of Economic Thought (pp. 28–45). Malden, MA.

Edit: Fixed a broken link.