You're right that surface tension is strong enough to support small objects that normally would not float, such as needles. You can remove surface tension by adding a little bit of dish soap to the water. Why not try an experiment where you float a toothpick on soapy water in a clear glass, and float a needle in a clear glass of pure (non-soapy) water, and see which one sinks deeper into the surface? As long as the toothpick and the needle have about the same mass, you should be able to see which force is stronger.
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