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The weighted differential invariant signature is developed to deliver more geometrical information than the signature, by combining the signature manifold with invariant measurements that capture the size of local continuous and discrete symmetries. As a consequence, the weighted signature becomes an attractive tool for the task of distinguishing between signature congruent submanifolds, which have the property that they are globally inequivalent, yet possess identical signature manifolds. Properties and relationships between such submanifolds are discussed and how these affect the weighted signature.