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I'm not sure if SymSpell already has support for weighted edit distance. If so, please tell me how to use it.
Otherwise, I suggest to add this as another possible distance metric, in addition to Levenshtein and Damerau-Levenshtein. The implementation itself shouldn't be problematic: just use the weight matrix instead of the default unit cost. The matrix is input to the constructor, and for command line use it can be stored in a file. (I could in principle do it myself, but I don't know C#)