Couldn't you just put all the weights in a lookup table, and then iterate once over the characters of the string?  Something like this:

my %weight = (
    A => 0.6562,
    B => 0.3571,
    #...          
    z => 0.42,
);

for my $ch (split //, $string) {
    $count += $tbsz * $weight{$ch};
}
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Or (if the string is huge)

...
while ($string =~ /(.)/gs) {
    $count += $tbsz * $weight{$1};
}
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(And if ord($ch) of the characters is within a narrow range (such as ASCII), you could also use an array, and store the weights under $array[ord($ch)] — which might be a tad faster than a hash.)