There's no need to for two nested loops. That will get really slow when %hash gets big.

use strict;
use warnings;
use utf8::all;

my %hash = (
    the   => 5,
    good  => 3,
    The   => 2,
    Bad   => 2,
    uGly  => 1,
    uglY  => 1,
    École => 1,
);

for my $key (keys %hash)
{
    next unless $key =~ /^\p{Uppercase_letter}/;
    my $lckey = lc $key;
    $hash{$lckey} += delete $hash{$key} if exists $hash{$lckey};
}

for my $key (sort {$hash{$b} <=> $hash{$a}} keys %hash)
{
    print "$key\t$hash{$key}\n";
}
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Update: replaced /^[A-Z]/ match with a Unicode-aware regexp.