In order for you to be motionless in the pool, the total force on your body must be zero (thanks, Newton). When you’re in the pool, gravity doesn’t disappear. It’s still pulling you down. Which means something must be pushing back up.
You could (rightly) claim that the water is pushing you back up. But then there would be more force pushing down on the water. The water isn’t accelerating down, so something must be pushing it back up (it’s the bottom of the pool).
When you get in the pool you displace some water. This causes the water level to rise slightly. Each square centimetre on the bottom of the pool now has a taller column of water above it. That taller column is heavier, and so applies a greater force on the bottom of the pool. So you getting in increases the pressure exerted on the bottom, and so the entire pool carries your weight.
If the pool was already full then some water would slosh over the sides, and that amount of water would weigh the same as you, so the total weight of water + person in the pool would stay the same.
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