Actually array elements are binded okay, problem is hidden in other place.

The point is - when you did -textvariable=>$arr[$i], Tk used those scalars as a references to Entry contents.

But after your assignment to entire @data something, you have new different scalars in there!

But if you'll do

          @data[0..$#data] = ( 'a'..'x');
[download]

your code will work as you desired to!

Below is working code snippet for you to try:

use strict;
use Tk;
use Tk::Table;

my $mw = tkinit;
my @data = ( "init", "init", "init", "init" );

my $tableWidget = $mw->Table->form(-top=>'%0', -bottom=>['%100',-20], 
+-left=>'%0', -right=>'%100');
my $btn = $mw->Button(
  -command=>\&update,
)->form(-top=>$tableWidget, -bottom=>'%100', -left=>'%0', -right=>'%10
+0');
my @headers = 'a'..'k';
my $e;

  for ( my $row=0; $row<2; $row++ ) {
          for( my $col=0; $col<$#headers+1; $col++) {
                  my $e;
                  if( $row == 0 ) {
                          $e = $tableWidget->Button ( 
                                  -relief         => "groove", 
                                  -justify        => "left", 
                                  -text           => $headers[$col], 
                                  -state          => 'active',
                                  -width => length($headers[$col])
                          ); 
                  } else {
                          $e = $tableWidget->Entry ( 
#                                  -width        => $lens[$col], 
                                  -textvariable => \$data[$col]
                          );
                  }
                  $tableWidget->put( $row, $col, $e );
          }
  }



  sub update {
          @data[0..$#data] = ( 'a'..'x');
  }

  MainLoop;
[download]

Best wishes,
Baboon
PS.Weasel is stooped.