I figured I'd impart some of what I've learned over the last year on the Island - weather wise:
January - March: Cool mornings, afternoons in the mid 70- mid 80. Often nice beach weather, ocean a brisk 79 and often with strong currents. Pretty busy season for tourism here on the Island.
April - May: Mornings can still be cool but often 80/90 in the afternoon, the evenings still cool off nicely. Ocean is starting to warm to the 80's and the currents are starting to die off. A beautiful time to visit Cozumel. The winter high season stats to taper off and things become less crazy on the Island.
June - August. Very HOT. Not good for people without air conditioning. This would be the time I'd most like to come on vacation if I was staying in an air-conditioned hotel (aren't they all). The Ocean temp is up to 82/83. Great for diving, warm water, warm surface intervals, warm nights out - no sweater for dinner. August does start to cool off noticeably. The rainy and Hurricane seasons officially begin in June. I think this year has been particularly dry but August has brought a good few storms which start to give relief to the heat. Tourism fairly high with Texans escaping their summer heat!
September - October. Peak rainy season. I arrived in September last year and it rained almost solidly from September 15-Oct 15. The ocean is still warm for diving and the air temperature is still high. Good to visit if you are lucky enough to miss the rain. Low season - great deals to be had if you don't mind a little rain between your sun.
November- December. Tail end of November stating to really cool off. Sweaters and jeans creep into every day use. Less rain. Mornings and evenings cool but often very hot beach days. The Ocean starts to chill back to 79 by the end of the year. December is a high month for tourism which stays high through April spring break.
I've been lucky enough so far not to have experienced any real hurricane activity. This winter is expected to bring a moderate to strong El Nino (a periodic warming of the seas in the eastern Pacific). This can often suppress hurricane activity, so hopefully this will not be a bad hurricane season.