At the airport when getting on a plane I have had to produce proof of my residency when using a one way ticket to Belize. It's not at this end that they care, it's the airline that cares. If you were entering Belize on a one way ticket and Belize considered you an undesirable then the airline would have to pick up the tab for returning you to your point of origin.
If you are staying more than 30 days and you go to check in with immigration to extend your visitors visa you may have to prove that you have enough funds to pay for a return ticket or to produce the return ticket itself.