I discovered the Photon Freedom Microlight at Gossamer Gear a year or two ago and it’s been part of my regular hiking kit ever since. This incredibly little LED light weighs a mere 6 grams (0.2 oz) and can easily replace that clunker of a head lamp you are wearing today. It comes with a detachable hat clip that you can wear on a baseball style cap or clip to a bandana for night hiking or doing camp chores, and lasts 10 hours on a single lithium battery. The light comes with a brightness control that lets you make it brighter or dimmer, as well as a setting that flashes an SOS pattern and that the manufacturer claims can be seen a mile away.
My only complaint with this light is that they are incredibly easy to lose, and I find them sometimes a year later inside a tent or at the bottom of a backpack. So, in addition to a clip, I thread some very lightweight cord around the plastic eye on the tail of the light and wear it around my neck when in camp to avoid losing it. I also carry a second LED called a Skunklight that is marginally heavier (0.6), but is solar powered just in case I lose the Photon, and to avoid having to depend so much or carry extra batteries.
Disclosure: The author owns this product and purchased it using their own funds.