I permanently sewed my little headlamp to my hat.
I like the PETZL e+Lite (0.8 oz with the band removed). There is a simple metal wire that is used as an attachment system. But, it's awkward. It feels like it takes some angst with my fingernails to get it on a hat, and it's really hard in the dark.
And - I have a really simple lightweight pile hat, (1.2 oz). Now, for a mere 2 ounces, I have both forever connected.
Here's my nerdy gimmick. I clamped the light on the hat, and then sewed it in place. Now it's permanently attached to my hat. Easy!
If it's dark enough to need a light, I don't need my sun at with a brim. If it's cold enough to need my hat, it's probably dark. I never have to search for a tiny lamp in my pack (But, I still need to search for my hat)