Using gnu find, I think this is what you want. It finds all real files and not directories (-type f), and for each one prints the filename (%p), a tab (\t), the size in kilobytes (%k), the suffix " KB", and then a newline (\n).
find . -type f -printf '%p\t%k KB\n'
If the printf command doesn't format things the way you want, you can use exec, followed by the command you want to execute on each file. Use {} for the filename, and terminate the command with a semicolon (;). On most shells, all three of those characters should be escaped with a backslash.
Here's a simple solution that finds and prints them out using "ls -lh", which will show you the size in human-readable form (k for kilobytes, M for megabytes):
find . -type f -exec ls -lh \{\} \;
As yet another alternative, "wc -c" will print the number of characters (bytes) in the file:
find . -type f -exec wc -c \{\} \;