Why did Kubrick have several duplicates in The Shining?

One reason is so that each could "reflect" on the other and bring it to your attention more.

The 2 girls - possibly for the 2 daughters of the previous caretaker that were murdered - a "double" doubling. Could also represent "doppelganger" and seeing double (reference to alcohol's effect) as well as other doubles and dualities discussed below.

The 2 women - the young one to lure Jack into the room, the older one as the reality of what the young one had become, once Jack had been lured. Another kind of double/duality seen in this film - past/present, young/old, natural/supernatural. Also the lovely seductress/evil hag.

2 Jacks - the past, historical Jack and the future (present) Jack, as a future reflection of the previous Jack, and yet an imperfect one. Because the future Jack had choices yet to-be-made and chose to stay there each time, whether through fear or weakness or whatever.

2 Grady's - he mirrors the 2 people that Jack is - the mysterious man in the photo and the current Jack, husband and father to Wendy and Danny, respectively. He even has 2 names - Delbert and Charles, again an unsettling, imperfect match to keep the audience off-balance.

The film is all about dualities - past/present, real/imaginary, sane/insane, diseased/healthy, natural/supernatural, truth/deceipt, young/old, conscious/unconscious/ subconscious, mortality/immortality, surface/hidden, shadow/substance and visible/invisible not to mention dark/light, Jekyll/Hyde, good/evil.

These different types of dualities appear in different kinds of doubles - reflected, reversed, double letters in names (Overlook, Hallorann, Ullman, Danny and Torrance, even Johnny), in numbers doubled-reflected-reversed, even double doubles (the girls), doubling back (in time as well as retracing footsteps in the hedge maze), and redoubling of efforts (to escape and destroy). Some say these were efforts to disorient the viewer as well as to self-reflect, since many of the doublings and reflections do not exactly line up or mirror each other. Kubrick at his unsettling best.

Another recurring theme in this film is the labyrinth - from the hotel interior to the hedge maze outside, to the intricate and labyrinthine way he weaves the doubles, dualities and duplicity throughout his retelling of this tale (yet another imperfect and somewhat duplicitous reflection).

Here's a site that gives more insight:

http://www.imdb.com/title/tt0081505/faq

ADDED:

My 1000th answer on Y!A!!! =)

He wanted it to be that way? Either way, does it matter? Still doesn't change the fact that it's a good movie.