Even in 83 degree water you body will lose heat and given enough time, you will begin to show signs of hypothermia. So just because you "feel" fine with a thin suit on, doesn't mean it is enough. Safety first, it's always better to err on the side of caution.
Most DM's, because of diving all the time, get chilled more than us tourists do, so you will see them wearing a 3 mil with a vest or even another thin suit over/under it. A lot even wear hoods.
But for visitors, the 3mm seems to be the norm for Cozumel, you may not need that much protection most of the time, but you will most likely be more comfortable with it. On deeper wall dives in particular, you can hit some thermoclines that can give you a good chill. I've even hit some on Columbia Shallows at <30' that have given me the 'wiggles'. And depending on how long your going to be there and how much diving you are going to do, later in the trip you may be happy you had the extra thickness.
I'm pretty warm blooded and don't chill easily, and I dove Coz with a .5 mil for years, wearing a short sleeve surfing rash shirt under it, (April/May & Sept), with only an occational, late week chill issues.
I moved up to a 3 mil a couple of years ago and have been much more comfortable with it, but still after about 4 days of diving, I start looking for the rash shirt.