I also have a YBR 125 and was out yesterday fighting the wind and the rain. I do agree that it is a very light bike and it does get affected badly by the winds but by far the best solution is to cut your speed a bit, the bike is much easier to handle in winds at lower speeds. It may mean you have an impatient car sitting on your tail but that's far better that than risking veering into the opposite carraigeway.
I'm about to go out in the next 30 mins and there are 60mph gusts out there today, needless to say I'll be going a bit slower than normal
Ride safe, and enjoy.