I did a test a 1024x768 PNG vs the Same PNG at 2048x1536. 299k vs 664k. So for raster images it more than doubles the footprint, however if you use vector assets there should be little impact.
Edit: It is also interesting to see that the ~ 2x increase in the size of the PNG can be explained by PNG's run length encoding. When you double the pixels in each direction, RLE should readily compress the horizontal pixel replication but not the vertical pixel replication.