One way is to count the number of consecutive lines that start with a +- or += (just in case for some reason you have normal lines that start with a +. Hopefully legit lines won't start with += or +-. If they do, you'll have to lengthen the regex). If you get more than one, the file is deemed empty and we skip it. Note I skip the lines that have the separators and don't print them.

use warnings;
use strict;

my @files = qw(a.txt b.txt);

for my $file (@files){

    open my $fh, '<', $file or die $!;

    my $sep = 0;

    print "working on file $file\n";

    while (<$fh>){

        if (/^\+[-=]/){
            $sep++;

            if ($sep > 1){
                print "skipping $file\n";
                last;
            }
            next;
        }

        $sep--;

        chomp;
        print "$_\n";
    }
}
[download]

file a.txt:

+=======+=======+============+============+============+
+-------+-------+------------+------------+------------+
[download]

file b.txt:

+=======+=======+============+============+============+
line 1
line 2
+-------+-------+------------+------------+------------+
[download]

output:

working on file a.txt
skipping a.txt
working on file b.txt
line 1
line 2
[download]