There used to be flights between Cancun and Belize City. AeroCaribe for one, and another airline before that. If I recall correctly, Tropic even flew it at one time.
But there hasn't been any flights in the past three or four years. There really wasn't much demand. Belize is viewed as a backwater by most airlines, Mexican or otherwise.
The same thing holds for Cancun-Chetumal -- over the years various airlines have flown the route and most have discontinued service after a year or two. Buses make more sense on that route.
Though from Cancun (or Coz/Playa) to Belize City it is virtually a full day of travel and even if you fly from Corozal to San Pedro you're still spending a full day. Unless I'm spending time in the Yucatan, it's not worth it to me to take two full days, one going and one coming, getting from Mexico to Belize.
More interesting is what's happening with Tikal Jets. They're now flying three times a week from Flores to Belize City, jets and cheaper than Tropic and Maya Island. And now they're adding flights from Belize City to Havana. They already do Flores-Cancun and Flores-Guatemala City, among other destinations. And now Continental is flying Houston-Flores. I think we'll see more options coming from Guate rather than Mexico.