As a fellow heavy sweater (and no, for me, it's not a weight thing), I can sympathize. My uniforms would come out soaked. First off, your uniform getting soaked in sweat is not necessarily a bad thing, at least up to a point. One of the reasons why most martial arts uniforms are cotton, or silk, is that it's a material that wicks sweat away from your body to the outside layers. Sweating cools you down by air circulating over the sweat and the sweat evaporating. If your dobok is scotch-guarded, it's not wicking the sweat away, so you're not getting cooled. Your body won't cool off, and you'll sweat more. In extreme cases, you get plastic or rubber suits that force you to dehydrate (even today, competitive fighters use this method to temporarily drop their weight to reach a given weight class). So you want your outfit to wick the sweat to the outside, but ideally to not get sodden with sweat, whereupon you have extra weight and extra irritation.
As Steve is alluding to above, that may mean a lighter uniform. Less thickness means there's less distance for the moisture to wick up. It may mean trying to control for environmental humidity by practicing indoors, or not after a rainstorm (the higher humidity makes it more difficult for the sweat to evaporate). It might just mean training until your body gets more efficient and generates less waste heat (which, paradoxically, generally involves training in hot conditions).
As to how to keep your outfit white, you won't have much luck doing so while you're working out (you're sweating more than the other people. That's a fact). What you can do is control for the situation going into a practice and the situation going out. One thing you can do going in is to try to sweat clean. Avoid foods that cause you to sweat with a strong scent (this is individual to the practitioner, but most people have more of a problem with things like asparagus or meats). Try to avoid putting on too much deodorant. I know it sounds weird since antiperspirant is in the name, but when you are going to be sweating hard, it just create a waxy buildup. Drink sufficient fluids to dilute the waste products your body will be outputting. After practice, you may want to rinse your outfit in clean water to wash out the skin cells and other stuff you shed in your sweat. Then, either toss the outfit in a dryer or hang it up in an area where it will dry efficiently. Don't toss it into a closet or on the floor.
With those steps, you'll reduce the amount of staining you sustain and, in time, your sweating will get better as you get more fit and your body recognizes that it doesn't need to sweat as much to keep you cool.