I'm sure it's been done before in the other answers, and maybe even more efficiently, but this is what I think you're trying to get to:

#!/bin/perl
#if your program doesn't begin with this, you deserve to fail...
use strict;
# Data::Dumper not used in example, 
# but you always need it when you expand the module :-) 
use Data::Dumper;

# you can either hardcode all atomic weights in ...
# ..or read them from a data file/ database
my %weights = (
   'C' => 12.0,
   'O' => 16.0,
   'Co' => 58.933195,
   'H' => 1.008
   );

my @test = ( 'C12H22O11' );

for my $form (@test) {
    my @array = $form =~ /[A-Z][a-z]*\d*/ig;

    my $weight = getweight(@array);
    print "Weight of @array : $weight\n";
}


sub getweight {
       my @atoms =@_;
       my $weight = 0.0;

       for my $element (@atoms) {
          if ($element =~ /([A-Z][a-z]*)(\d*)/) {
             my $eweight = $weights{$1};
             my $mult = $2 || 1;
             $weight += ($eweight*$mult);
             print STDERR "Adding $1 ($eweight)* $mult\n";
          }
       }
       print STDERR "Molecule: @atoms\n";

       return $weight;
}

[download]

Feel free to modify for your purposes and correct naming,read atomic weights from a file etc.

Output from above program:

Adding C (12)* 12
Adding H (1.008)* 22
Adding O (16)* 11
Molecule: C12 H22 O11
Weight of C12 H22 O11 : 342.176

[download]

Updated to reflect the fact that some transuranic elements have 3 letter identifiers, not just two. :-)

Also updated to reflect suggestions by Kenosis and others below....

Whilst adequate for the indicated input, the method of parsing and atomic weight calculation is a little lightweight and basic, and doesn't handle more complex molecules, so consider using Chemistry::Mol or a similar package if you want to get round the flaws that have been indicated below....

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