Are there any "gyms" or places to work out (with weights) on Caye Caulker?

No gyms. Most of the bench sets that have been brought to the island are in a pile of rust. Plenty of other ways to get a workout:

1) Find a concrete building going up and offer to help mix, lift and pour concrete.
2) Find a buddy and do some laps around the island carrying a 200hp outboard. Scratch that, cops may get suspicious...
3) Juggle coconuts
4) Bench press 5 gal bottles (full)
5) Wrestle a crocodile by the airstrip.

I'm sure there may be other good suggestions...

Monday thru Thursday at 5 pm there are excersize classes abouve the Village Council, a mixture of arobics, step, yoga, stretching, floor exercizes and weights, classes are a little over an hour and pretty fast paced, the cost is $1.00 US a session.

You don't need 5 gallon bottles. Belikin bottles even empty are about the heaviest I've seen. I'd recommend them.

Buy a case of Belikin and a 5-gallon jug of water from the distributor and instead of having it delivered, carry it to your abode.