First of all, I don't understand if you want all three-letter immediately repeated words, as your OPed regex
    /\b(\w\w\w)\s\g1\b/;/
implies, or all three-letter words that are repeated anywhere else in the string, as your code implies.

In the spirit of the second interpretation (and counting them) (requires Perl version 5.10+ for  \g-1 construct):

c:\@Work\Perl>perl -wMstrict -MData::Dump -le
"use 5.010;
 ;;
 my $term = 'Dit is het eerste het is xhetx xhet hetx niet het laatste
+ Dit';
 ;;
 my $word = qr{ \b \w{3} \b }xms;
 ;;
 my %repeats;
 while ($term =~ m{ ($word) (?= .*? (?= $word) \g-1) }xmsg) {
   $repeats{$1}++;
   }
 ;;
 dd \%repeats;
"
{ Dit => 1, het => 2 }
[download]

Updates:

1. Added info about 5.10+ requirement.
2. BTW, the "regex"  /\b(\w\w\w)\s\g1\b/;/ doesn't actually compile. It looks like it might be a piece of something else, e.g., a substitution:
       s/\b(\w\w\w)\s\g1\b/;/
   (update: or maybe the / at the end is completely extraneous and the statement  /\b(\w\w\w)\s\g1\b/; was intended — that would work)
3. When I wrote "Change the definition of  $word to whatever best suits your requirements" above, what I had in mind was that any  $word definition used in the context of the
       m{ ($word) (?= .*? (?= $word) \g-1) }xmsg
   match would be assured to match repeated words per my understanding of the OP. Not so, and it's easy to manufacture a counterexample. Of course, it's also easy to fix the counterexample to avoid the problem, but the fix requires knowledge of internal details of the  $word definition, and this is exactly what I was trying to avoid. In a further iteration, I can come up with a match regex that seems to fulfill all my (admittedly rather arbitrary) requirements, but it's not well tested and I don't really love it as I should. So as always, Caveat Programmor.