Yay for fancy comp sci terms. It is NP-complete! (or is it "NP hard"?)

Given 100 numbers, this code finds a likely-optimal solution in about 1 second. If you are unlucky, it can spend a very long time after that not finding any better solutions. :)

#!/usr/bin/perl -w
use strict;

sub halfWeights
{
    my @weights= sort { $b <=> $a } @_;
    my $dist= 0;
    $dist += $_ for @weights;
    $dist /= 2;
    my $best= $dist;
    my @sol;
    my @idx= ( 0 );
    while( 1 ) {
        $dist -= $weights[$idx[-1]];
        for( abs($dist) ) {
            if( $_ < $best ) {
                $best= $_;
                @sol= @idx;
                printf STDERR "%+g: %s\n", $_, join( ", ", @weights[@i
+dx] );
                return @weights[ @sol ]
                    if( 0 == $_ );
            }
        }
        if( 0 < $dist ) {
            push @idx, 1 + $idx[-1]
        } else {
            $dist += $weights[ $idx[-1]++ ];
        }
        while( @weights <= $idx[-1] ) {
            pop @idx;
            return @weights[ @sol ]
                if( 1 == @idx );
            $dist += $weights[ $idx[-1]++ ];
        }
    }
}

@ARGV= ( 100 )
    if( ! @ARGV );
push @ARGV, $ARGV[0]*$ARGV[0]
    if( 1 == @ARGV );
if( 2 == @ARGV ) {
    my $cnt= shift @ARGV;
    my $max= shift @ARGV;
    push @ARGV, 1 + int rand($max)
        while( @ARGV < $cnt );
} elsif( 3 == @ARGV ) {
    my $cnt= shift @ARGV;
    while( @ARGV < $cnt ) {
        push @ARGV, $ARGV[-2] + $ARGV[-1];
    }
}
halfWeights( @ARGV );
[download]

Note that if you have fractional weights, then the way that things are computed will likely cause a growing accumulation of errors that won't impact the likely-optimal solution much but could cause serious misrepresentation of how close other solutions really are if you wait the hundreds of years and more that it could spend contemplating them.