This may be a random approach as it depends on how your files are listed by ls . Proposal on hand reverses the order of files and prints the last name of files of identical size, then. BTW, file name is $9 on my ls -l version.To remove files, use command substitution like $(...):
ls -lr | awk '
$1!~/^d/ {++size[$5]; name[$5]=$9}
END {for (i in size) if (size > 1) print name}
'