Yours is not an uncommon problem (we have four questions on this subject in the hopper right now) but there are a variety of solutions. The reason meringues weep is that they are undercooked on the bottom, and some of the moisture that is held in suspension in the egg foam seeps out all over the pie filling. So the first part of the solution is never to let your filling cool before smoothing on the meringue. In fact, the filling should be piping hot to help set the bottom of the meringue. That may not be enough, though.
option many people take is to add a teaspoon of cornstarch to the sugar before beating it into the meringue. The cornstarch absorbs extra moisture, and has the added bonus of keeping the whites from becoming overbeaten. Shirley Corriher, author of Cookwise (Canada, UK), uses a slightly different method. She blends a tablespoon of cornstarch with 1/3 cup of water, heats it until it forms a thick gel, and then adds it to the meringue a tablespoon at a time after all the sugar has been added. She says this keeps the meringue from shrinking, lowers the chance that beads will form on the surface, and makes a meringue that is tender and easy to cut smoothly.
Roland Meisner, pastry chef at the White House, is said to sprinkle very fine cake crumbs over the surface of the pie filling before adding the meringue. If the meringue weeps, the crumbs absorb the moisture, and, whether or not there is weeping, the crumbs dissolve into the pie.
Rose Levy Beranbaum, author of The Pie & Pastry Bible (Canada, UK), says a method devised by Michael Field called for adding 1/4 teaspoon of the nutritional supplement bone meal (yum, yum) for every three eggs. It works brilliantly, Beranbaum says, except that there is a perceptible grittiness that one does not normally associate with lovely homemade pies. She is looking to bone-meal manufacturers of the world to produce a finer powder, but we aren’t holding our collective breath.
Beranbaum does not care for the cornstarch slurry method either, by the way, as she says it “compromises the etherial lightness of the meringue.” She would rather use a more stable Italian meringue if it comes to that.
So there are several options, any of which may involve some degree of compromise. You may have to do a little experimenting to see which method you like the best.