In 2016, a breakthrough result of Chechik and Wulff-Nilsen [SODA '16] established that every n-node graph G has a (1+ε)(2k−1)-spanner of lightness Oε(n1/k), and recent followup work by Le and Solomon [STOC '23] generalized the proof strategy and improved the dependence on ε. We give a new proof of this result, with the improved ε-dependence. Our proof is a direct analysis of the often-studied greedy spanner, and can be viewed as an extension of the folklore Moore bounds used to analyze spanner sparsity.