Your code is very very hard to read. I have reformatted it as the following to make the structure more apparent:

my $up = "UPDATE Prior_to_CI_calc_A_$region 
            SET SUM_wi           = $SUM_Weight_wi, 
                Sum_wixi_x_1000  = $SUM_wixi_x_1000_fill, 
                Sum_wi2xi_x_1000 = $SUM_wi2xi_x_1000_fill
            FROM Prior_to_CI_calc_A_$region A 
            WHERE     A.Aggregated_area LIKE '$Aggregated_area_fill' 
                  AND A.Cause LIKE '$Cause_fill'
";
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You are creating SQL on-the-fly and I'm not sure your SQL syntax is correct, as I don't know the combination statement modifiers you use. I think that your error is most likely because one of your several embedded variables is empty or undefined. I recommend that you follow one of the two following paths:

• Implement full SQL statement logging. Whenever you submit any query to your SQL server, log the full query into a logfile. DBI has logging facilities that you can use for that.
• Switch your queries from embedded values to queries using placeholders. I think that Super Search should give you a lot of examples, and your above query would be split up like the following:

  sub update_region {
    my ($region) = @_;
    my $table  = "Prior_to_CI_calc_A_$region";
    sprintf "UPDATE %s 
            SET SUM_wi           = ? ,
                Sum_wixi_x_1000  = ? , 
                Sum_wi2xi_x_1000 = ?
            FROM %s A 
            WHERE     A.Aggregated_area LIKE ? 
                  AND A.Cause           LIKE ?
", $table, $table;
  };

  my $region = "foo";
  my $query = $dbh->prepare(update_region($region));

  $query->execute(1,2,3,'US','unknown');
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