While I applaud your use of references to create complex data structures, you can save some memory and speed by operating on the hash directly:

sub sort_by_value {
    my $hash = shift;
    sort {$hash->{$a} <=> $hash->{$b}  } keys %$hash;
}
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I won't ask why you declare @keys and then immediately clobber it. :) (I often forget to delete test code, too.)