If you know the answer, I would appreciate it if you could explain it to me.
I can only provide the bloody obvious, sorry (by which I mean that I'm not to terribly knowledgeable). Others here can probably fill you in on the greater implications.
As to pegged currencies, yes some countries do peg their currencies to the dollar (for instance, IIRC, at one point Argentina pegged their currency to the U.S. Dollar --though they don't seem to do that any longer).
Without doing any real research (because I'm too lazy), if you take a look at
http://www.exchangerate.com/ you should see that all of the currencies listed there show a non-zero number in the 'Change' column (with the exception of the U.S. Dollar because, for some unfathomable reason, it is comparing the U.S. Dollar to itself). Any such change would denote a currency not pegged to the U.S. Dollar (with the exception of being in the middle of changing --i.e. today it's pegged and yesterday it wasn't pegged or it was pegged at a different level). One of the currencies listed there with non-zero change is the Canadian Dollar.
Compare and contrast with the chart of Central American currencies (which includes the Belize Dollar) that can be found at
http://www.exchangerate.com/world_rates.html?cont=Central%20America/Caribbean . Looking at it now, I see a whole bunch of currencies (including Belize's --which looks to have, as you indicated, a 2:1 relationship with the U.S. Dollar) which have a value of zero in the 'Change' column. I suspect all or most of these currencies are going to be pegged to the dollar.
As to the greater implications (this is where others would be of more help than me) I suppose the import/export implications will be similar to those which may befall us with the specifics in each instance being very dependent on who they are selling to and who they're buying from. For instance, if you are selling bananas and tourism to Europeans, the weakening dollar will have an effect (you become cheaper and more attractive seller to Europeans). If you're importing automobiles from the Japanese, it will have an effect (the cars will become more expensive). If, however, most of your imports and exports are to people from the U.S.A., there will be no
direct effects. However indirect effects will exist. If the weakened dollar has pernicious effects on the U.S. economy which cause Americans to cut their spending (or conversely increase spending if the Dollar's fall turns out to be a good thing --which I reckon would be unlikely) that will be bad for the country (or good, if it turned out that a weak dollar was a good thing for the U.S.). Naturally the implications of a more realistic mixed import/export market would fall somewhere in between.
And, of course, I would imagine that if the people in charge of the economies of these countries with currencies pegged to the U.S. Dollar felt their current arrangement was no longer beneficial, they'd have the option to change it to something more beneficial (by making their currency stand on it's own, by pegging it at a different rate to the U.S. Dollar or by pegging it to a different currency altogether --or even to a basket of currencies).
On Edit: Expanded on the "bloody obvious" as I decided I may sound like I'm being too much of a smart ass with that phrasing.