Perhaps vegetable or olive oil for staining it to look like sweat? You can also use watered down acrylic paints too. Black, Tan, Rust, and Clay colors work well.
Under the arms (obviously), between the shoulder blades, lower back, chest, and crease of the arms tend to be the areas that sweat tends to show up the most.
Just remember to take your time and do it in layers. Once the layers build up it will look more realistic, plus lessen the chance of you making a change you can't go back on if you were to go heavy on the weathering. Better to go light and add more than too heavy and you can't change it back.