Don’t forget to look at headlamp weights. For example, the Jaxman E1 weighs 140g with a battery. I wouldn’t want that heavy beast on my forehead while running or extended periods of time. A skilhunt h03 weighs about 70g with the battery. A much better option imho.
Ummm its that including the headlamp strap? 
Without headlamp strap for both examples.
H03 weighs 44g without battery (light only, no battery)
E1 weighs 83g without magnet, or 94g with magnet (light only, no battery)
Zebralight H600 series weighs 39g, (light only, no battery)
Thats about double the weight for the Jaxman E1, apples for apples.
Once you add in the bat and head strap its not double the weight
I mean one does use a headlamp with a head strap and a bat
You are right, the difference is less proportionally when you add everything into the equation, but what adds weight and bounce potential to a headlamp is not the strap, but just the light and battery. Not trying to argue a technicality, but just a point to be aware of that usually leads to discomfort and dissatisfaction of a headlamp. Many people prefer AA/16340 headlamps because they find 18650 format too heavy. The Jaxman E1 will weigh the same as an H03 if the H03 ran off 2 x 18650. Technically, not double the weight, but a significant and noticeable difference.
Slip-up. Edited.
I won't comment on the weight thing except that I'm not really that afraid of. Certain headlamps use a battery carrying box at the back of the head, I like that; gives balance to the thing.
How about this?
https://www.aliexpress.com/item/32763339560.html
XML-L2 
It may need some modifications, but wonder about the beam profile. 