First of all, we sweat as a method of normalizing/reducing our body temperature caused by the situ temperature, outside of our bodies. This mechanism, is primarily completed with thanks to the Eccrine sweat glands - those that cover the greatest majority of the body and hence, are the most essential in this context.
Sweating is classed as 'evaporative heat loss' so, the correct conditions have to apply in order for the mechanism to effectively occur.
Humidity: The common perception is that we sweat less in hot and humid conditions since, "the sweat just sits there", inferring that we are perspiring at a slower rate. However, it's the complete opposite. This is because, in the stated environmental conditions, the ambient water vapor pressure is greater and resultantly, the body needs to increase the area effected by perspiration -- the sweat rate increases -- thus to match the same effect that you'd experience in hot, dry conditions. The affinity for the evaporation product to attach to molecules in the air is less due, to there being more water molecules already present in the air. It's a bit like how water in cells moves from areas of high potential to low water potential.
The body can more efficiently cool itself in this environment. This is due to fact that dry air has a greater affinity for water molecules so, the sweat will evaporate quicker. Additionally, this has a knock-on affect on salivary glands and furtherly, the humidity of your essential respiratory organ, the lungs - causing dryness. This is very prevalent when breathing heavily e.g. in exercise.
This is very similar to hygroscopy.
To conclude, you need to drink more water in hot, humid environment than the contrary.
If my answer is too "generalized"; i apologize.