I am a lightweight guy (about 155lbs). I am also a college level ski racer. I have struggled with the disadvantage that my weight puts me at for some time now. As a lighter skier you have to find other skills or muscles that you can develop that will make it so you are at less of a disadvantage.
I have worked off the slopes to develop amazing balance on and off skis, as well as developing strength in my lower and upper body. I only weigh 155lbs but i can squat almost 300lbs, and bench about 185lbs. I also do an extensive leg work out to keep my legs in very good shape in comparison to the big guys i race against. They usually will not be able to lift proportionally the amounts of weight that i can handle, therefore have a harder time on the snow holding their skis on the snow - eliminating chatter, bending the ski... etc.
I have also worked to develop my carving in and out of the course so i can keep my line clean when other big guys just cant make the turns. Leg strength is important here as well... but it isnt as important as the lack of weight. Down a pitch especially, a heavier person will gain more speed than a lighter one. Therefore if they dont have the strength to compensate they will have to put on the brakes or not carve clean turns so they do not end up going too fast. The lighter skier will not be traveling as fast, but can often maintain a carve in a tighter line than the larger person can. This will allow the lighter skier to carry more speed out of a technical section of the course.
I have also found an advantage from my size and build. I am a short guy (only 5'7") but i am fairly stocky and muscular (7% body fat the last time i checked). This allows me to have a lower center of gravity than a taller lanky guy. When carving turns this makes a huge difference in the amount of angluation i can get... thus will let me carry a lot of speed through turns... and accelerate out of turns.
Now as for a short flat hill... This is tough. A light guy stands almost no chance of catching a heavier guy... especially if a heavier guy sets the course. They will often set turns that they know people of their body type will be able to carry speed through. If the course is set with any kind of technical section you will be able to have a more fair race. Work on how clean you can carve your turns and also how to accelerate out of your turns. Riding a flat ski where you can helps as well, since the base is faster than the edges. Try to take a line through the course that no heavy guy could match. Carve it clean, tight, and fast.
(Ideally i would like to grow 2 inches and gain 25lbs, but i dont think that will be happening so ill make due with what i have. At 5'9" and 180lbs and the same amount of strength proportionally that i have now i think i would be a VERY competitive racer).