section start marker
dear (13)
dear friends (22)
love (10)
dear friend (10)
loved (3)
dearly loved (1)
friends (1)

section start marker
competes in the games (1)
contend (1)
fight (2)
fought (1)
make every effort (1)
strive (1)
wrestling (1)

##</code><code>##

use strict;
use warnings;

open my $file, '<', 'input.txt' or die $!;

process_file($file);

exit 0;

sub process_file {
    my ($fh) = @_;

    while ( my $line = <$fh> ) {
        print $line;

        if ( $line =~ /section start marker/ ) {
            $line = handle_section($fh);
            redo if defined $line;
        }
    }
}

sub handle_section {
    my ($fh) = @_;
    my ( @entries, $line );

    while ( $line = <$fh> ) {
        last unless $line =~ m{
            ( [^(]+ ) # 1 anything except opening paren
            \s        #   space
            \(        #   opening paren
            ( \d+   ) # 2 number
        }x;

        push @entries, [ pack( 'Na*', $2, $1 ), $line ];
    }

    print map  { $_->[1] }
          sort { $a->[0] cmp $b->[0] } @entries;

    return $line;
}

##</code><code>##

section start marker
dearly loved (1)
friends (1)
loved (3)
dear friend (10)
love (10)
dear (13)
dear friends (22)

section start marker
competes in the games (1)
contend (1)
fought (1)
make every effort (1)
strive (1)
wrestling (1)
fight (2)