Why were The Matrix 2 and The Matrix 3 released in the same year?

The Matrix 2 and The Matrix 3 were filmed together (or "back to back").

Prior to the filming of The Matrix 2 and The Matrix 3, this was a pretty uncommon practice but did occur. In recent years it has become much more commonplace when it is known there will be multiple movies.

Release dates of movies filmed together have spanned anywhere from 3 months to 3 years apart (although Superman’s release was delayed due to staff differences rather than being planned that way).

Here is a, probably not comprehensive, list of movies filmed together with the intent of separate releases) along with their release dates (list courtesty of Wikipedia - missing dates added via google search):

• Superman: The Movie and Superman II were filmed simultaneously in 1977 to be a two-part epic. Released in December 1978 and December 1981. (3yrs)
• Back to the Future Part II and Back to the Future Part III were in production from February 1989 until March 1990. Released Nov 1989 and May 1990 (6mo)
• Critters 3 and Critters 4 were shot back to back. Released Dec 1991/Aug 1992 (9mo)
• The Matrix Reloaded and The Matrix Revolutions were filmed back to back. Released May 2003 / November 2003. (6mo)
• Kill Bill was filmed as one film and split into two volumes. Released Oct 2003/April 2004 (6mo)
• The Lord of the Rings trilogy was filmed entirely over 274 days in New Zealand from October 1999 until December 2000. Each part released 1yr apart from 2001 to 2003.
• Pirates of the Caribbean: Dead Man's Chest and Pirates of the Caribbean: At World's End were filmed back-to-back from February 2005 until January 2007. Released July 2006 / May 2007. (1yr)
• Anaconda 3: Offspring and Anacondas: Trail of Blood were filmed back-to-back. Released July 2008/Feb 2009 (8mo)
• The Girl Who Played with Fire and The Girl Who Kicked the Hornets' Nest were filmed back-to-back. Released July 2010/Oct 2010 (3mo)
• Harry Potter and the Deathly Hallows – Part 1 and Part 2 were filmed entirely from February 2009 to June 2010. Released November 2010 / July 2011. (6mo)
• The Twilight Saga: Breaking Dawn – Part 1 and Part 2 were filmed back to back. Released Nov 2011 / Nov 2012. (1yr)
• The Hobbit trilogy was shot back-to-back in New Zealand from March 2011 until July 2012. Released 1yr apart from 2012 to 2014.
• The Hunger Games: Mockingjay – Part 1 and Part 2 were filmed back-to-back. Released Nov 2014 / Nov 2015 (1yr)

As a result, while your question asks why (which I haven't answered), it also gives the basis that this is unusual where that seemingly is not the case. And unless the producers/directors/film company stops by to inform us, it would just be speculation.

But since you asked, my guess is that the decision is based primarily on which release cycle is estimated to bring in the most money.

Well, the second answer on a similar question on Quora says this:

Originally, the Wachowskis wanted to release The Matrix Reloaded in May and The Matrix Revolutions in June. This release schedule may have helped the perception of the sequels, as they were really one large movie, split in two. By the time November came around, the good will the third part may have had was gone, thanks in large part to critics not understanding the film.

Unfortunately, there is no citation. If true, this suggests from a story telling point of view, the Wachowskis wanted to have as small a gap as possible between releases.