Is water at the bottom of the ocean thicker / heavier than water at the top?

Not significantly. From Wikipedia:

Liquid water can be assumed to be incompressible for most purposes: its compressibility ranges from 4.4 to 5.1×10−10 Pa−1 in ordinary conditions. Even in oceans at 4 km depth, where the pressure is 400 atm, water suffers only a 1.8% decrease in volume.