Belize has never been a wealthy country. It used to be called British Honduras. It was a British colony. It became independent 36 years ago. I can only think you are confusing it with another country. If this crime has put you off moving to Belize, I suspect Belize is probably not for you. In the same way America is not for me. The constant mass shootings make me very worried about going to America. You can be sitting in a theater or restaurant and someone just walks in and starts shooting everyone. I can say that is not something I ever worry about in Belize.
Maybe it's comparing apples to oranges, but I found this 2012 report interesting. It's not terribly lengthy so it's worthwhile to "click to read more".
http://www.washingtontimes.com/news/2012/jan/16/tale-of-two-small-countries/