Yes! It is more than a light resemblance or impression. Let me quote three authors at length. First, Max Weber himself:
Laws are important and valuable in the exact natural sciences, in the measure that those sciences are universally valid. For the knowledge of historical phenomena in their concreteness, the most general laws, because they are most devoid of content are also the least valuable. The more comprehensive the validity,–or scope–of a term, the more it leads us away from the richness of reality since in order to include the common elements of the largest possible number of phenomena, it must necessarily be as abstract as possible and hence devoid of content. In the cultural sciences, the knowledge of the universal or general is never valuable in itself. (Max Weber, 1904, Objectivity of Social Science and Social Policy)
Second, Milton Friedman:
In so far as a theory can be said to have “assumptions” at all, and in so far as their “realism” can be judged independently of the validity of predictions, the relation between the significance of a theory and the “realism” of its “assumptions” is almost the opposite of that suggested by the view under criticism. Truly important and significant hypotheses will be found to have “assumptions” that are wildly inaccurate descriptive representations of reality, and, in general, the more significant the theory, the more unrealistic the assumptions (in this sense). (Milton Friedman, 1953, The Methodology of Positive Economics)
And third, Robert Lucas:
A second variation is easy to carry out. Rather than consider a worker- entrepreneur, one could separate these functions, introduce firms, and consider labor and product markets separately. In the present context, this would introduce a distinction between wages and prices, and raise the issue of risk-allocating arrangements between employers and workers. It would also permit the study of possibly different information sets for firms and workers. None of these questions is without interest, but all are, in my opinion, peripheral for business cycle theory. Observed real wages are not constant over the cycle, but neither do they exhibit consistent pro- or countercyclical tendencies. This suggests that any attempt to assign systematic real wage movements a central role in an explanation of business cycles is doomed to failure. Accordingly, I will proceed as though the real wage were fixed, using the terms “wages” and “prices” interchangeably. (Robert Lucas, 1977, Understanding Business Cycles)
These short texts are so Weberian in style and attitude that I always thought that the authors must have been influenced by Weber somehow. The answer was provided by Ross B. Emmett, who has been studying the role of Frank Hyneman Knight in the evolution of Chicago Economics, i.e. the intellectual environment for both Friedman and Lucas. Knight translated Max Weber’s General Economic History (1927), so he was strongly influenced by Weber and he was completely aware of the Weberian methodology. And… Knight was one of Friedman’s professors in Chicago, so Friedman must have been well-educated in Weber. This is the intellectual foundation of the relationship between Weber and Friedman – and Lucas, whose professor was Friedman himself. It is not accidentally that both of them created methodologies that bear strong resemblance to Weber’s methodological works. Now it is time to prove that Friedman and Lucas diverged in methodological terms, since Friedman made efforts to re-interpret Weber in an instrumentalist way. However, for me it is out of question that Lucas was far from being instrumentalist.