Hi Momo88,
Weeping can result from the sugar not being dissolved properly, overbeating & if the weather is humid.
Make sure your egg whites are super fresh & at room temperature, & all your utensils spotlessly clean. Don't use eggs staright out of the fridge.
My Nana used to add a pinch of salt, as the whites were being beaten, & just as the mixture started to bubble & change colour. Apparently this helps to reduce the temperature of the whites. You could also try beating the whites over a bain-marie (pot of gently simmering water), but don't let the water touch the bowl, otherwise you'll cook your egg whites. This helps to stabilize the mixture.
Also, I'm not sure what sort of recipe you have, but try one with cream of tartar in it, I believe this helps to stabilize the meringue as well.
To check if the sugar has dissolved, rub a little of the mixture between your fingers & if it feels a little gritty, it needs more beating. Don't forget the mixture needs to be really stiff & glossy, & oven temperature no more than 120C, for around 1&1/4hrs. Meringues are dried out, not cooked, so leaving them in the oven after this time to cool completely is really important.
When I need meringues (or a pavlova), I usually make them the night before, & leave them in the oven overnight to cool completely.
Hope these help 