Weather Station Location To Zip Code Cross Reference

I’m trying to map zipcodes to their closest weather station (see example station code and name below) but am having trouble finding a source. I’ve been scouring the NOAA website which offers some maps to let you look up one zip code at a time but I can’t locate any sort of tables or similar user-friendly data. The NOAA reports that contain these stations also have latitude and longitude fields but matching to a zipcode on that basis seems pretty tricky. Does anyone know of a data source or have suggestions?

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