All other things being equal (density of rocks, latitude, etc.), you would weigh VERY slightly more. Being closer to the Earth's core, while being on the surface, you would experience a slight increase in the pull of gravity, compared to what you would experience at sea level. You would need an incredibly accurate scale to measure the change, but for some of us, even an incredibly tiny weight loss is still a weight loss.

That would be slightly offset by your buoyancy in the slightly denser air surrounding you, but not enough to completely negate it.

Now, if you started digging downwards, your weight would start to decrease, because you would have less mass below you pulling down, and more mass above you, pulling up. By the time you reached the Earth's core (assuming that it was possible), the pull would be equal from all directions, making you weightless.