Recently I have had to scale up the dimensions of a gif image by a factor of 2, this resulted in an increase of the file size by about 8 times. While this is not a complete surprise, I can't help but think there should be a format that scales well with such an operation.
Compression in GIF images is quite primitive and cannot take advantage of redundancy created by upscaling of the image.
I you resize without anti-aliasing then well-optimized PNG shouldn't grow by much.
If you resize with anti-aliasing then convert the image to JPEG, as this will create lots of new colors and soft edges that are best handled by JPEG.