If you're making what is known as a cold French meringue, in which basically the egg whites and some cream of tartar are beaten until frothy and then the sugar is added in slow increments, the meringue spread on top of a pie, then browned under a broiler, the sugar is much less stable than in a Swiss or Italian meringue. Sugar is extremely hygroscopic, meaning that in solution, it will literally extract moisture from the air in order to keep itself in solution. There is your weeping problem.
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