Fire itself does not have weight, but it does experience the force of gravity. The upward movement of fire you observe when you light a matchstick is due to convection.
When you light a matchstick, the heat from the flame causes the surrounding air to become hot and rise. This creates a convection current, where the hot air moves upwards while the cooler air moves downwards to replace it. The flame follows the direction of the rising hot air, which is why it appears to go up.
The force of gravity acts on the gases and particles involved in the combustion process, including the hot air and the products of combustion. However, the buoyant force resulting from the temperature difference in the air overwhelms the force of gravity, causing the fire to rise.
It's important to note that while fire itself doesn't have weight, the materials involved in the combustion process (such as the matchstick, fuel, and oxygen) do have weight and are subject to gravity.