Usually both. I usually bring the lightest camera I am willing to use AND suck it up and bare the weight, because when you're hiking, every ounce adds up. Of course, how much weight you can manage will be determined by the terrain, how far you plan to hike each day, if you have to carry water with you, and you're own physical fitness.
That being said, there's no point to going on a photographic hike only to bring a camera that won't take pictures of the quality you want, just because it's small and lightweight. I'd suggest taking as few of lenses as possible, and get a sturdy, yet lightweight tripod to cut down on weight. Then take the camera you want.