You said you're travelling by boat, but "BZE" is the abbreviation for the International airport outside Belize City.
If you're leaving from AC by private boat, go to the Immigration office in San Pedro -- get your passport stamped and pay the departure fees. When you arrive at Mahahual, you'll have to report to Immigration. I think there is an Immigration office there for the cruise ships -- go to the cruise ship port and ask. You should get an FMM tourist card and have your passport stamped. When you fly out, you'll have to pay the DNI/Tourist Tax at Cancun airport.
How will you continue north -- by boat or on land?