Find and remove all empty files

find /path/to/mountpoint -empty -type f -delete

If your find does not have -delete option, replace it with -exec rm '{}' ';'

If you want to delete all empty files except for files directly under / run:

find / -mindepth 2 -empty -type f -delete

If you want to delete all empty files, but skip whole /root directory run

find / \( -path /root -prune \) -empty -type f -delete

find . -size 0 -print.

replace -print with -delete and . with the directory you need, but execute carefully, it will really delete all empty files.