This is possible - only slightly tricky. You must add the property to the catalog, spec, and project (it must be named EXACTLY the same in all - case sensitive). It helps to create a spec template with all your custom properties and create all future specs from it so you don't have to add the custom props each time.
First add the prop to your catalog:

Note: you cannot change/modify this property for each size in the catalog editor. It will only show one value in the general properties area - ignore this:

To modify the values, you must export the full catalog to Excel and edit it there:

After making your changes, import the Excel values.
Next, add the property to your spec(s).

Now when you add parts to the spec, the new catalog property will be visible in the spec editor.

Next, add the property to your project - here again a project template with custom props is helpful.
Now, when items are added from the spec, the custom size property is available.
Example 1:
Example 2:
