Word Error Rate weights
The various weighting systems are a domain-speific attempt to adapt the raw edit distance metric into something more "perceptual". The needs &amp; error tolerances for one domain, say large vocab open speech, may be different from the command-and-control, "assistant" systems.

Humans differentially weigh different types of ASR errors and are less forgiving with errors (like say insertions) which may distort the meaning of the transcription.

Have a look at this paper: Predicting Human Perceived Accuracy of ASR Systems