My pilot lite will lite and stay on. When I turn the thermostat up to fire the burners the pilot lite stays the same. Shouldn't the pilot lite flame increase so the thermocoupling will heat up to tell the gas valve to suply gas to the burners.

The pilot light gas flow is fixed by an adjustment. The flame must cover the end of the thermocouple about 3/8" from tip and no more. Too much gas will cause the thermocouple to quit working and gas will turn off.