It’s actually considerably less fuel in less time but the point stands, the burn rate is faster and the thrust is higher on the AIM-120A/B. I don’t know why people expect missiles to just accelerate faster and faster after each iteration, maybe it is R-27R/ER syndrome.
The yellow book does indeed suggest that the WPU-16 motor used on the AIM-120C-5 has about 5 kg more Net Explosive Weight (NEW) than the WPU-6 used on the AIM-120B.
Though I think it has been debated before whether the yellow book is entirely accurate?
16km “pitbull” range is against test specimen of Mig-15. Against larger, 3rd/4th gen airframes seeker often starts tracking target as far as 20-22km away. In general ARH seekers is bit of a schrodringer case, activating itself exactly when game calculates it will start tracking reliably.
Even without going into IRL missile properties, first Dev build version of C5, something that sat in game files since ARH were added was both HOBS improvement and range improvement, latter achieved with serious lofting trajectory out of otherwise sidegrade motor.