Yes, the aperture grille (hundreds of wires and a metal frame holding them in tension) is itself heavier than a traditional shadow mask.

However, aperture grilles also use differently-shaped glass from shadow masks. The screens are only curved horizontally like a cylinder rather than on both axes like a sphere. This requires thicker, heavier glass to hold the vacuum.

Later flat-glass shadow-mask tubes were much closer in weight to flat Trinitrons.