because of convection currents and the warm air rises and the cold air sinks down causing the Basketball to not bounce as high
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The atoms in the air inside the ball are continuously bouncing around. When temperatures become warm those atoms bounce faster, but when it becomes cold, atoms slow down making the ball not bounce as high.
Because when gas gas is colder, in the same volume, the pressure is lower. Because of the lower pressure, the ball does not bounce as well.
There is an equation: PV = nrT. P is pressure, V is volume, n is the amount of gas (it's actually the number of molecules of gas), r is a constant and T is temperature. So if V, n and r remains constant, if the temperature goes up, the pressure will go up, and the converse is also true.
Warm weather as in warmer weather the air molecules in the Basketball are more active and give better pressure.
probably has something to do with the floor you are bouncing the ball on! the bounce differs from wood floor or whatever the floor is outside!