Respectfully, if you need to " When pushing the handle forward, you are using both your arms and your back, the musculature in your back being quite significant." it sounds like some lubrication to overcome the friction is in order either in the headlight bucket, HL actuator arm or the cable. Just looking at used parts that I have sold, the part with the potentially most resistance is the cable, and I can easily slide a cable in my two hands.Well, at the margin, it does help push the handle forward. When the doors are closed (lamps off), the spring is under tension. In pushing the handle forward to open the doors, the cable moves in the direction in which the spring is relaxed -- in effect, the spring is helping pull the end of the cable back into the casing.
As I said, it is not a big spring, so it would take a pretty fine instrument to measure the difference in forces between opening and closing the headlamp doors.
But in reality, the difference you feel is simply a matter of kinesiology. When pushing the handle forward, you are using both your arms and your back, the musculature in your back being quite significant. When closing the doors, your back plays little to no part -- its all arm and shoulder, with perhaps some leverage gained off a leg.