If there's a sudden increase in headwind, you get an increase in lift and drag. The drag reduces the airspeed to equilibrium and the performance increase disappears. The opposite happens when there's a loss of headwind - lift and drag both decrease, the aeroplane sinks, accelerates and finds equilibrium again.
A light aircraft has very little momentum and equilibrium is rapidly restored. This is why you can fly an approach in a Cessna 152 in gusty conditions with no real difficulty, though it will be a bit 'sporting'. In a larger aeroplane, large thrust changes can be needed to prevent airspeed increases and ballooning followed by airspeed decreases and sink. In gusty conditions I'd rather be in a Cessna than a 737.