Owing to the proliferation of user-generated videos on the Internet, blind video quality assessment (BVQA) at the edge attracts growing attention. The usage of deep-learning-based methods is restricted to be applied at the edge due to their large model sizes and high computational complexity. In light of this, a novel lightweight BVQA method called GreenBVQA is proposed in this work. GreenBVQA features a small model size, low computational complexity, and high performance. Its processing pipeline includes: video data cropping, unsupervised representation generation, supervised feature selection, and mean-opinion-score (MOS) regression and ensembles. We conduct experimental evaluations on three BVQA datasets and show that GreenBVQA can offer state-of-the-art performance in the Pearson Linear Correlation Coefficient (PLCC) and the Spearman Rank Order Correlation Coefficient (SROCC) metrics while demanding significantly smaller model sizes and lower computational complexity. Thus, GreenBVQA is well-suited for edge devices.