A quality bar of handmade soap will often "sweat" in humid weather due to the high content of natural humectants. A humectant is a substance that readily absorbs moisture from its surroundings and handmade soap is high in glycerin. 

Glycerin, a humectant that provides amazing benefits to soap, is a natural byproduct of saponification, the chemical reaction that produces soap.  In commercial soaps, the glycerin is removed and used to produce commercial lotions.

Handmade soaps, rich in natural glycerin, are the most moisturizing soaps you can find! When you wash with natural soap there is a thin layer of natural glycerin left behind, which will help draw moisture to your skin to keep it hydrated and prevent dryness.  The general health of the skin relates directly to its moisture content. All natural handmade soaps can help the skin maintain a moisture balance while nourishing the skin.

When natural soap sits out in humid conditions, the glycerin in the soap draws moisture out of the air and onto the soap which then appears as little beads of water on your soap bar--like morning dew on blades of grass. 

So the sweating is actually moisture from the air that the glycerin attracts, not moisture coming from inside the soap. The more humid the environment and the more humectants in the soap, the more likely you'll experience this phenomenon.