Of the various types of handles you will find on a custom knife, the lightest weight handles are going to be in the hardwood category. Since softwoods are not typically known as good knife handle material, you can expect your knife handles to be made out of hard woods like maple or burl which are very nice, beautiful, serviceable wooden handles.
Other light, durable, custom knife handles are often made out of plastics like micarta, which has become very popular over the last few years. Micarta is comfortable like wood, is very durable, and has become affordable. It also is produced with many interesting designs and styles.
There are a wide variety of knives listed at http://www.JustCustomKnives.com. Drop by and take a look at their custom knives!
Another strong, relatively light handle material is bone. Though these days many bone handles are actually factory produced bone substitutes, it is still a relatively popular handle material that can last for many decades of use if properly cared for.
The lightest type of knife handle would be what is called a skeletonized handle, which means it is drilled out to be lighter, and doesnt have an actual handle material added to it, only the milled tang.
Pictured knife has a stag horn handle created by Serkovs Forge, his store is located on JustCustomKnives.com