Some scientists are making the case that global warming is contributing to an increase in earthquake activity by making the ocean water warmer, and therefore, heavier.
Correct me if I am wrong but I know things expand with increased heat but I'm not sure about them getting heavier...
The increased heat content does actually make it more 'massive', hence heavier. But this is a relativistic effect.
This is where that famous E = mc^2 comes in. But it's not detectable (5 parts in 100 trillion per degree K). So she's talking bollocks.
P.S. I should have expanded on that a little. In Einstein's theory, energy has an equivalent mass associated with it. Heat is energy, so that has associated mass. The equation relating the two is E = mc^2, where c is the speed of light, about 3 x 10^8 metres per second. If a kilogram of water has its temperature raised by one degree K (one degree Celsius, same thing) then the heat energy contained in that water has risen by about 4,200 joules. (This is just one of those things that can easily be measured in a laboratory. It's a standard measurement/experiment in O-Level school physics.)
By the equation, the mass equivalent of that heat is given by m = E/c^2, i.e. the increase in mass = 4200 / (3 x 10^8)^2 = 4200 / (9 x 10^16) = about 4.7 x 10^-14 kilograms. So it does get heavier but it's undetectable, pretty much.
For different reasons (centrifugal forces, distance from Earth's centre, and inhomogeneity in Earth's crustal density) your own weight ('heaviness' )can vary by as much as about 0.5%, depending on where you are on the planet. Of course the same applies to water too. You never notice it though. The effect above is 100 billion times weaker.