Is microUSB connector used for charging inherently lighter than USB-C solution?
tl; dr: USB-C is no benefit for this application. Micro-B is more than enough and will be cheaper / lighter.

The flashlight (torch in Brit-speak) is self-limiting its charge rate based on the battery size and its "1C" charge rate. If you exceed that rate the battery can be damaged through overheating.

More about charging rate here: https://batteryuniversity.com/learn/article/what_is_the_c_rate

And here: https://batteryuniversity.com/learn/article/charging_lithium_ion_batteries

A small headlamp like the one shown would not benefit from USB-C power delivery, as it has a correspondingly small battery and thus, a limited charging rate.

The specification for this lamp is a 680mAh battery. If we assume it's one cell (3.8V), then we can infer that the max 5V draw for a 1C charge is:


680mA * 3.8V/5V = 516mA from USB


So ordinary USB 2 (500mA) is pretty close to adequate for this lamp; and USB3 (900mA) is more than enough. Note also that USB BC 1.2 can support up to 2.4A. That's plenty.