How do you refit clothing?

Negative. A sewing kit would be enough to allow the reinforcing/refitting action that is currently a single option. They should definitely be separate.

A tailor’s kit fits more thread in (allowing you to try the desired operation on clothing for longer) and allows you to do proper reinforcing: currently you can pad the item with kelvar or leather, for increased protection but also increased encumberance.

To find a tailor’s kit, look through clothing stores. Houses sometimes have one.