You should read perlintro, and start over, that code is awful.

#!/usr/bin/perl --

use strict;
use warnings;
use CGI();
use CGI::Carp qw(fatalsToBrowser);

my $html = <<'__HTML__';

all your html , exactly as you want it

__HTML__

my $freaky_number=int(rand(9999)) + 1;
my $check_number=rand(9999);
my $k_weather = "../weather_/".$freaky_number.".txt";


if( open DDATA, ">$k_weather" ){
    print DDATA $html;
    close DDATA;
} else {
    warn "Can't open output file $k_weather: $!";
}

my $q = new CGI;
print $q->header(), $html;
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