It's because of the high-altitude IR windows in the absorption spectrum as I understand it. If CO2 is added at 1 km it really has no effect there since CO2 absorption in these windows is mostly saturated already, but as you climb to higher altitudes ~12 km the lower pressures mean those windows clear up - but a relatively small increase in CO2 starts filling in these windows. The best source I've found for explaining this at the non-technical level is:
https://history.aip.org/climate/Radmath.htm#L_0165