I said: Weather-wise, it is likewise after most of the nortes and before hurricane season. Plus, May is the height of the fishing season.
I went to Cozumel several times before I started diving, and it was for the fishing in May. Migrating billfish (marlin and sailfish) are usually in the area in May, and May is also the peak of the dorado (aka mahi mahi, aka dolphin) fishing season. It's why there are several fishing tournaments in the vicinity in May. I still fish when I am there, and the serious fisherpersons in my group (my sister and her husband, both non-divers) set our dates every year by consulting the phases of the moon, slinging around a dead cat, tossing some burnt chicken bones, and whatever other gris-gris they can come up with.
Mainly we fish for dorado and billfish, but we also catch the occasional barracuda, wahoo, blackfin tuna, and Spanish mackerel. The billfish we catch we release, but the dorado we keep and give the filets to the boat crew, hotel personnel, and other friends on the island.
Thank you for the fishing information.