Lately, there has been a lot of interest in the weighted Birkhoff averages of form \[A_{w,\phi}(x)=\lim_{n\to\infty} \frac 1n \sum_{i=0}^{n-1} w_i \phi(T^ix),\] where $\phi$ is a potential and $(w_i)$ is a fixed sequence of real numbers (weights). In this talk I'll present results (joint with Ruxi Shi and Balazs Barany) about the multifractal spectrum of the weighted Birkhoff averages.