Given multiple source word embeddings learnt using diverse algorithms and lexical resources, meta word embedding learning methods attempt to learn more accurate and wide-coverage word embeddings. Prior work on meta-embedding has repeatedly discovered that simple vector concatenation of the source embeddings to be a competitive baseline. However, it remains unclear as to why and when simple vector concatenation can produce accurate meta-embeddings. We show that weighted concatenation can be seen as a spectrum matching operation between each source embedding and the meta-embedding, minimising the pairwise inner-product loss. Following this theoretical analysis, we propose two \emph{unsupervised} methods to learn the optimal concatenation weights for creating meta-embeddings from a given set of source embeddings. Experimental results on multiple benchmark datasets show that the proposed weighted concatenated meta-embedding methods outperform previously proposed meta-embedding learning methods.