Weight or wing loading?

Does wing loading have any affect on thermalling ability of a glider (pilot's ability is another topic)?

I am ignoring here the smaller turn radius, and so greater ability of a lighter wing-loaded glider to work narrow-diameter thermals. In a given thermal with a diameter that can be worked with identical airspeed and bank angle by two gliders, one with lower wing loading, does smaller wing loading have any affect on the rate at which the gliders climb in the thermal?

Given gliders each weighing 800 lbs., but one has a wing loading just 75% of the other, wouldn't they both still require a minimum of 800 lbs of thermal force to hold altitude and wouldn't they both climb at the same rate in stronger but identical (whatever that means) thermal force? I'm remembering F=ma (more usefully, a = F/m) from physics classes MANY years ago. "Wing loading", or whatever its equivalent would be, does not appear in the force formula.

Whatever the answer may be it certainly will not improve my poor thermalling. Just curious.