The article said "the weight of the atmosphere was growing". Yet the number of atoms of carbon and oxygen on the planet is fixed, with none being created or destroyed, only redistributed. If the atmosphere is "getting heavier", the solid part of the planet is getting lighter.
Actually, earth gains weight with all the meteorites and space dust it sweeps up. Maybe the extra weight is what's causing that component of the slowing rotation. Most probably, there are enough observational and computational errors in the models that make this figure invisible among the statistical "noise".