Not sure if you're still looking, but here's one product that I've been using for the past 8 months or so. The Panther Vision LED Cap (link is for example, didn't buy hat from there) has two LEDs and a switch built into the brim of the cap. Runs off two CR2032 batteries. The cap weighs about 7 grams more than my previous hat. The level of light is comparable to other coin cell LED lights. I use it as a backup light source - when I'm changing batteries in another light, trips to the toilet tree, and rooting around in a pack at night. Not well-suited for reading or other close-in work (threading needles) because the lights are at the edge of the brim.

My main light is a Rayovac headlamp - single AA cell 1/2-watt with diffuser. Any small headlamp will work with a ball cap if you don't pull your cap down to your eyebrows. I like the combination because it's convenient. My dome is chrome so I always wear a hat, therefore I always have a light. When I need more light (or light for a long period) I use the headlamp.

However, if you're stuck on the cap you have and don't want to change the way you wear it to accommodate a headlamp, there are several ball cap brim clip-on lights available from places like Walmart and Target. I have one that has UV LEDs - really good for hunting scorpions at night or hunting a lunch-stealing co-worker during the day (little sprinkle of UV powder in the sack, then walk around looking for the tell-tale handprints). Walmart's a good place to buy-and-try. Don't like it - return it.