The problem was on line 26. I changed ->pack(-side => packwith... to top:

#!/usr/bin/perl

use strict;
use warnings;
use Tk;

require Tk::BrowseEntry;

my $mw=MainWindow->new;
my $f=$mw->Frame(-borderwidth=>2)->pack(-side=>'top', -fill=>'x');
my (@packwith) =();

my $numwidgets=4;

for(my $i=0;$i<$numwidgets;$i++)
{
    my $be = $f->BrowseEntry(-label => "Widget $i", -choices => ["left
+", "right", "top", "bottom"], 
                -variable => \$packwith[$i], -browsecmd => \&repack) -
+> pack( -ipady=>20);
    }            
my $b=$f->Button(-text =>"repack", -command=> \&repack)->pack(-side =>
+ "bottom");

my $tl=$mw->Toplevel(-title=>"output");    

for (my $i=0;$i<$numwidgets;$i++) {
    my $b=$tl->Button(-text=> "Button $i")->pack(-side => 'top');
}
MainLoop;

sub repack {
    my @slaves = $tl->packSlaves;
    my $j=0;
    foreach (@slaves) {
        $_->packForget;
        $_->pack(-text => "Button ".$j, -side=>\$packwith[$j++]);
    }
}
[download]