No the mass, and therefore weight, are not greatly relevant. What matters is the elasticity.
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A tennis ball does bounce higher!!!:]] x
A heated tennis ball bounces higher because the hot air inside the ball is lighter than the air around the ball therefore giving the tennis ball the ability to bounce higher.
Because of gravity, a ball with a larger mass will take more energy to bounce than a small ball (of the same material) will, so a small one will usually bounce higher.
If you were bouncing them both, a basketball would bounce higher.