we know that
A vessel full of water weighs 16.5kg
when the vessel is half full, it weights 10.5kg
so
16.5 kg-10.5 kg=6 kg is the weight of half water
the weight of full water=6kg*2------> 12 kg
so
the weight of the vessel=A vessel full of water-the weight of a full water
the weight of the vessel=16.5 kg-12kg=4.5 kg
the answer is
the weight of the vessel is 4.5 kg