my @flat_data;

for my $file (keys %hoh){
  for my $letter (keys %{$hoh{$file}}){
    my $weight    = $hoh{$file}{$letter}{weight};
    my $intensity = $hoh{$file}{$letter}{intensity};
    push @flat_data, 
      "weight: $weight intensity $intensity Filename: $file";
  }
}

print "$_\n" for sort @flat_data;

##</code><code>##

---------- Capture Output ----------
> "c:\perl\bin\perl.exe" _new.pl
weight: 1000 intensity 4 Filename: FILENAME3
weight: 2000 intensity 7 Filename: FILENAME2
weight: 3000 intensity 2 Filename: FILENAME1
weight: 4000 intensity 3 Filename: FILENAME1
weight: 5000 intensity 3 Filename: FILENAME2
weight: 6000 intensity 3 Filename: FILENAME3

> Terminated with exit code 0.