so clearly not spring break time. Although if you are at the Ritz, the amount of partiers will be low. Then tend to stay in the same areas. If I am in a place where there´s typically a lot of spring breakers, I will happily pony up extra $ to stay in the nicer places. The party kids don´t want to "waste" their money on nice hotels. I´ve never even felt like there was spring break going on the two times I was in Cancun during spring break.
Also I´ve been in cancun during fall break (oct). and Thanksgiving. For fall break, it rained all the time and we were told it was the rainy season--I´m not sure if that is entirely true, but it wasn´t awesome. They another year, we were there for Thanksgiving and the weather was simply amazing. We are probably going to go there again next year.
Honestly the best time for a quiet visit to Cancun would be the first few days after Labor Day or a couple of weeks before Memorial Day as most of the Spring Break party types would be in school and you'd most likely find an older less party minded crowd, although it is still Mexico ya know!!!!
Your weather in September will be warm and humid, getting that way in May, but there will usually be a nice breeze by the ocean. The Best Resorts in Cancun, Mexico | JW Marriott Cancun Resort & Spa is a lovely spot and not as pricey as the Ritz if that is a player in your decision. Also the Best Hotels in Cancun, Mexico | CasaMagna Marriott Cancun Resort which is right next door to the JW is a fine place as well, just not a JW. In fact the Ritz is pretty close as well to the other two.
Now, if you want to visit Mexico with perfect weather and less crowds maybe give the less than a year old take a look at the Cabo Resorts - Hotels | JW Marriott Los Cabos Beach Resort & Spa. We visited there last January arriving on the 3rd and the place was just about empty right after the holidays, very very quiet and the weather was in the low 80's every day with brilliant sunshine. The resort is not close to all the happenings and party spots of Cabo San Lucas, but to the east in a new upscale residential area close to the quaint city of San Jose' Del Cabo and about a 25 minute ride from the airport.
Hope some of this helps as I'm sure other Insiders will provide excellent tips for you to consider.