how much does one weigh at the center of the earth?

You are weightless at the center of the Earth (in as much as the question makes any sense).

That would be 0lbs. (or 0 Newtons).

The net some of forces (although gigantic) would be at equilibrium at the center of earth's mass (which is not exactly the center; earth is not a perfect sphere).

ebrownp is correct.

Edit: Weight is a force related to gravity/masses attracted to each other. The earth is not the only mass in the universe, and therefore, while the force of gravity exerted on you from earth would be negated (net force = 0), the force of gravity from other objects like the moon, sun, etc would still be present.

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In fact if I remember correctly and I do any place inside of an empty sphere would have zero g from the shell.