The answers for down-sampling have already been provided.
This answer relates to up-sampling using the full range. Here is a C99 snippet demonstrating how you can spread the error across the full range of your values:
#include <stdio.h>
int main(void)
{
for( int i = 0; i < 256; i++ ) {
unsigned short scaledVal = ((unsigned short)i << 8) + (unsigned short)i;
printf( "%8d%8hu\n", i, scaledVal );
}
return 0;
}
It's quite simple. You shift the value left by 8 and then add the original value back. That means every increase by 1 in the [0,255] range corresponds to an increase by 257 in the [0,65535] range.
I would like to point out that this might give worse results than you began with. For example, if you downsampled 65280 (0xff00) you would get 255, but then upsampling that would give 65535 (0xffff), which is a total error of 255. You will have similarly large errors across most of the higher end of your data range.
You might do better to abandon the notion of going back to the [0,65535] range, and instead round your values by half. That is, shift left and add 127. This means the error is uniform instead of skewed. Because you don't actually know what the original value was, the best you can do is estimate it with a value right in the centre.
To summarize, I think this is more mathematically correct:
unsigned short scaledVal = ((unsigned short)i << 8) + 127;