Video moment retrieval aims to localize moments in video corresponding to a given language query. To avoid the expensive cost of annotating the temporal moments, weakly-supervised VMR (wsVMR) systems have been studied. For such systems, generating a number of proposals as moment candidates and then selecting the most appropriate proposal has been a popular approach. These proposals are assumed to contain many distinguishable scenes in a video as candidates. However, existing proposals of wsVMR systems do not respect the varying numbers of scenes in each video, where the proposals are heuristically determined irrespective of the video. We argue that the retrieval system should be able to counter the complexities caused by varying numbers of scenes in each video. To this end, we present a novel concept of a retrieval system referred to as Scene Complexity Aware Network (SCANet), which measures the `scene complexity' of multiple scenes in each video and generates adaptive proposals responding to variable complexities of scenes in each video. Experimental results on three retrieval benchmarks (i.e., Charades-STA, ActivityNet, TVR) achieve state-of-the-art performances and demonstrate the effectiveness of incorporating the scene complexity.