Anyone know what this small Williams wrench would be for? Total length is approx 4 1/2"

could be a jaw wrench for a lathe or similar tool for another machine some machines had a rack on the side with holes the stub end went in the hole and stored the wrench when not in use.   jmho   bob w.

That's called an Offset Socket Wrench and the model number is a standard size denoting a 3/8" square opening.

They are used in industrial setting and I believe pipelayers may still use them for installing storm or sanitation sewers, drains, and water mains.

They are still made...

Thanks for the info