If you want to count overlapping matches, a plain regular expression as you wrote it isn't the easiest way to approach the problem.

Personally, I would simply iterate over the string either for each character or by resetting pos and using \G as documented in perlre:

use strict;
my $line= 'AAALVDENEC';
while( $line =~ /\G.*?(AA|AL|DA|DE|DV|VD|DW|QD|SD|HD|ED|DY|VE|EN|EI|KE
+|NV|VP|FV|SS|WK|KK)/igc ) {
    print sprintf 'Matched [%s] at %d', $1, pos($line);
    pos( $line )--;
}
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