I actually just figured this out yesterday. Here’s what I did:
First, I created an action that resized the image to the size I wanted. It contained 2 steps: 1) Fit Image to, then 2) Canvas size.
This generated the images in the sizes I needed.
Then I created a big action that took the original image and added as many layers to it as I needed resized copies. So, if I needed a picture in 10 different sizes, I would add 10 layers in the action.
The next step in the action was to re-name all of those layers.
Then, Select the base layer. Run the first resize action (still recording the big long action).
The picture is resized. Brilliant. Cmd+A, Cmd+C.
Go to the History tab, and click back THREE (3) steps. This will put the image and canvas back to where it was before you ran the resize action.
Click on the first new layer you created. Cmd+V, paste in the resized image.
Click the base layer, and repeat these steps until you’ve made all the resized images you want.
Stop recording big action.
Then, turn off the base layer and choose File>Scripts>Export Layers as Files. Make sure you have “Trim Files” selected.
And, BOOM!. You got yourself resized image files.