I suppose that he uses the data.resize when size is 64 because it takes too much time for the data loader to perform an on-demand scaling with a target dimension of 64.
On the other hand, on-demand data loader scaling from the original size to 128 or to 256 may take less time, so it’s pointless to do a pre-scale of all the images with data.resize. However, nothing prevents to do that. The resize it’s just to speed things up.
So, in the end, images are scaled by the DL from the original sizes to 128 and 256. As for the coefficient, I think it’s try and test to find a balance between quality and speed.
(These are my opinions, bear in mind I could be totally wrong 
)
Edit: found Jeremy’s answer here.