Note that I've added hash %is_selected for the Checkbuttons to have a 'memory' ( $is_selected{$item} will tell you whether the given item is required ). The moving of Buttons is achieved with manipulating the list itself (no hash necessary for that):

use Tk;

my @items=qw(State Dependency CalcTime Result FooState FooDependency F
+ooCalcTime FooResult BarState BarDependency BarCalcTime BarResult);
my %is_selected;

my $mw=new MainWindow;

my $item_width=15;
my $UP=1;
my $DOWN=-1;

my %attr_item=('-background'=>'#ffafaf');
my %attr_btn=('-background'=>'#afffaf','-activebackground'=>'#7aaa7a')
+;

my $text=$mw->Scrolled('Text',
    -insertontime=>0,
    -scrollbars=>'e',
    -width=>($item_width+15),
    -background=>'#efefef'
    )->pack;

my $first=1;

$text->tagConfigure('item',%attr_item);

&build;

MainLoop;

sub build
{

$text->delete('1.0','end');

foreach my $item (@items)
    {
    
    my $btn=$text->Checkbutton(%attr_item,
            -variable=>\$is_selected{$item},
            -onvalue=>1,
            -offvalue=>0,
            '-activebackground'=>'#ff7f7f'
            );
            
    my $up=$text->Button(-text=>'Up',-command=>[\&move,$item,$UP],%att
+r_btn);
    my $down=$text->Button(-text=>'Down',-command=>[\&move,$item,$DOWN
+],%attr_btn);

    $text->insert('1.0',"\n") unless $first; $first=0;
    
    $text->windowCreate('1.0',-window=>$up);
    $text->windowCreate('1.0',-window=>$down);
    $text->windowCreate('1.0',-window=>$btn);
    $text->insert('1.0',sprintf('%-'.$item_width.'s',$item));
    $text->tagAdd('item','1.0',"1.$item_width");
        
    }

}

sub move
{

my $what=shift;

my $dir=shift;

my ($index)=grep {$items[$_] eq $what} (0 .. $#items);

my $new_index=$index+$dir;
$new_index=0 if($new_index>=@items);
$new_index=@items-1 if $new_index<0;

my $temp=$items[$new_index];
$items[$new_index]=$items[$index];
$items[$index]=$temp;

&build;

}
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