The -z filetest works for me on *nix:

use warnings;
use strict;
my @files = <*.txt>;
for (@files) {
    if (-z $_) {
        print "File $_ is empty\n";
    }
    else {
        print "File $_ is not empty\n";
    }
}
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I have 3 files in my current directory. Only the file named "a.txt" is empty. When I run the program above, I get this output:

File a.txt is empty
File b.txt is not empty
File c.txt is not empty
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