2cyprus,
Like the rest of the respondents to your question I have set up my weather web site purely for myself, my friends and relatives plus as an additional source for the local volunteer bush fire brigades (if they wish to use it).
I suppose that Cyprus being in a reasonably popular tourist area you could try tying in with tourist organisations, hotels and the like; though I suspect that you would have to make it much more than just a weather site to convince others to pay for your product (e.g. links to historical sites, accommodation, tours and so on).
There is every chance that these areas are already well and truly covered by the tourist industry so you could be whistling in the wind - still, a bit of research and lateral thinking might (and I do mean might) result in some sort of income. Of course, even if you do manage that, it’ll be a site which includes weather information rather than a weather site per se and will involve much more work.
Good luck. If you do manage it then you’ll at least pay for some of your equipment and web costs.