Citizens and Permanent Residents of Belize don't pay anything. Visitors/tourists pay BZ$37.50 (US$18.75) payable in BZ$ or US$ at the land border. Departing by water taxi to Chetumal might be cheaper -- in this case, I think only the BZ$7.50 PACT fee is payable.
Visitors in transit from Belize to another country must pay the MX$262 fee for the FMM (visitor's card/form/visa/whatever). The fee is not paid at the border but at a bank before you depart Mexico although I think it can be paid at Cancun airport.
Departing from Cancun Airport
I've never paid anything. If there are any airport fees, they must have been included in the ticket price. If you haven't already paid the MX$262 FMM fee, you will be asked to pay.
An FMM should be issued on the plane before you land at Cancun. The fee should be included in the ticket price, so nothing more to pay.
Hand in the FMM form. There are no departure fees; nothing to pay at the border.
Nothing to pay.
The fees haven't been changing every few months, but beware of the scam at the land border where the Mexican immigration official has been asking for a departure of US$20. There is no departure fee from Mexico.