The Unabomber reached out. Thanks, Ted, you're not nuts at all. Every generation has their own boogeyman. After September 11th, 2001 Osama Bin Laden was the most wanted and most feared man in the world, up until the raid on his compound that left him dead.
In addition to not drinking enough water, water can be lost through sweat, vomiting, diarrhea and using the restroom. Many problems may occur when you don't drink enough water, including heatstroke, seizures and possibly death. The first complication of not drinking enough water is dehydration. Symptoms of dehydration may include thirst, sticky or dry mouth, tongue, lips and skin as well as a mild headache.
Now, I will likely be interrupted by Mother Nature and lose 1-2 lbs from the previous 32 oz glass of water I drank after my early workout. The easy answer is yes - drinking water does affect weight significantly enough to be seen on a scale immediately.