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Hot air rises! You created a convection current of air moving inwards towards the burning tea bag and rising up as a hot air column. The rocket could only rise once the tea bag became lighter (smoke has weight too!). Anyone who has seen a hot air balloon is quite aware of this basic principle.
Heating air adds more energy to the air molecules that make air up. These molecules with extra energy move around very quickly and become more separate from each other than in the cold, low energy, air. When you separate molecules you effectively have a less dense substance.
The rules within buoyancy make less dense substances rise above more dense substances... this makes the less dense hot air rise above the cold air. The process keeps working because the cooler surrounding air keeps coming towards the light and warming up. This is a simple demonstration of convection currents that exist in thunderstorms and ocean currents.
Put simply, a convection current is the transfer of heat energy by the movement or flow of a substance from one position to another.