Short answer: sugar that hasn’t fully dissolved, humidity, or spreading it onto a cold filling.
“Weeping” is those little beads of syrup that form on or under a meringue. It usually means the sugar didn’t dissolve fully into the whites, so add it gradually and whisk until the meringue is stiff, glossy and smooth (no grittiness when you rub a little between your fingers). Damp weather makes meringue sulk, so it’s not a job for a humid day. And spread or pipe your meringue onto a filling while the filling is still a touch warm, then bake or torch soon after — that helps it seal rather than sweat.
Related:toasted meringue tart · glossary:French meringue.