I have departed Mexico and entered Belize a few times without paying anything at the border on the Mexican side.
My understanding is that is no "exit tax" at all. There is a fee for the FMT tourist card that visitors get when they enter Mexico.
When you enter Mexico by air, you should be issued (on the plane) with a form called Forma Migratoria Para Turista, Transmigrante, Visitante Personade Negocios o Visitante Consejero – Internacion Aerea (in English: Migratory Form for Foreign Tourist, Transmigrant, Business Visitor or Councilor Visitor – Entrance by Air).
The fee for the FMT is usually included in the cost of the airline ticket, so there is nothing to pay on arrival in Mexico and nothing to pay at a bank.
If you entered Mexico by land, there is a similar FMT form. There are instructions on the back of the form stating that the fee must be paid at a bank before departing Mexico, and there's even a list of banks. I think the fee is about MX$280 (that's pesos).
The FMT allows a maximum stay of 180 days. When you go through immigration, the immigration officer will write in the actual number of days you can stay; it will be between 30 and 180 days depending on your nationality. Immigration will keep the top part of the FMT form, and you keep the bottom part with your passport.
When you leave Mexico via Chetumal by bus, the bus will stop at a small immigration booth on the Mexican side of the border. Passengers get off, without luggage, and present their passports with FMT to the immigration officer. He will ask (in Spanish) for MX$100 (that’s pesos) or sometimes US$10. If you pay, the immigration officer should stamp your part of the FMT form “doble entrada” and put it back in your passport. This stamped FMT will allow you to re-enter Mexico within the allotted time (30 to 180 days) without paying a new re-entry fee. I have heard of people saying that the officer took the money, and did not return the stamped card; beware of that.
You may choose not to pay the MX$100, but then immigration will keep your part of the form, and the next time you enter Mexico, you will have to pay the full fee for a new FMT. And the fee for the new FMT isn’t paid at the border, but at a bank.
Whenever I've gone through the procedure, the immigration officer has always just asked for the money, and other passengers on the bus just paid without knowing that they didn't have to pay if they weren't returning to Mexico. The immigration officers I've encountered have never displayed an ability to speak English, so visitors can't even ask about the fee, and think it is an "exit fee". And the bus drivers were not helpful in explaining the fee.
When I come to Belize through Chetumal, and if I don't intend on returning to Mexico within the 180 days, I say "no regresa" and don't pay anything.