Kinetic energy is the work needed to accelerate a mass. Wind defined as the velocity air (not the same as energy, as noted in comment).
However, the air moved by wind is a good example of kinetic energy, molecules are accelerated by a difference in pressure and moved. When the pressure difference decreases, the movement of molecules stop. So yes, the wind moves matter with weight.
However, weights of gases are somehow difficult to sense, as any gas would replace the weight of the air that normally surrounds us. The weight of the air can therefore be understood as the pressure generated by the weight of all the air above. Air particles moves from high pressure to low pressure and so the wind is formed.
A way to show how efficiently the wind is actually moving the air masses, is to consider how the wind can transport solid matter, sailing boats, wind mills and even sand and rocks. For example the Harmattan, a wind from the North that transport huge amounts of dust from Sahara to the coast of West Africa and the Atlantic Ocean. Other air borne sediments can form thick formations of Loess or other aeoloian formations as sand dunes. Also consider how the wind can move clouds and how all water in rivers and lakes therefore have been transported by the wind.
I hope that this, very simplified answer will make you more interested in meteorology and Earth science in general.