As you dig down you would get lighter and lighter on your feet.
Any mass you are below (within the sphere of Earth) will exert a gravitational pull in one direction, while the mass above you (also within the Earth) will exert an equal and opposite pull.
the pressure would never lessen, just increase slower.
The gravity at the center is zero, but the mass above you is not exerting just gravity force (which gets cancelled out by the opposite side), but also pressure (from the weight of it falling down).
This means the water pressure would steadily climb, but at a slower rate as you move nearer to the center, and will be at maximum at the very center.
Fun fact: Gravity doesn't decrease the entire way down! Only when you get to the core does it decrease monotonically: https://physics.stackexchange.com/questions/18446/how-does-g...