Thanks, George, for pointing me to this interesting discussion. I have been in touch with Fairweathers from Belize and others from Jamaica. I have also been contacted by a family in England whose ancestor was a Jamaican who emigrated to England.
I have a "collection" of Fairweathers from all over the world and am the representative for Fairweather in the Guild of One-Name Studies. Through them, I have been able to set up a DNA project at Family Tree DNA. So far, we have two Scottish descendants and one English participant. I hope to get many more Fairweather males to participate so we can continue to trace back the history of our name. Although they charge a fair amount to participate, the good thing is that you need no more than two men in any given line and that will show the DNA for all their brothers, fathers, cousins, etc. So the cost can be shared among several. If you are a female Fairweather, like I am, you can pay part of the cost for your brother or male cousin and thereby obtain the information for yourself.
http://tinyurl.com/FairweatherDNA
Please look at my webpage - I would love to get any Fairweather photos you have to add to it.
http://tinyurl.com/WorldwideFairweather

Pam