If you increase the pressure of a gas above the liquid, how does that affect the amount of gas dissolved in the liquid?

The solubility of gases depends on the pressure: an increase in pressure increases solubility, whereas a decrease in pressure decreases solubility. This statement is basically Henry's Law, which states that the solubility of a gas in a liquid is directly proportional to the pressure of that gas above the surface of the solution. This can be expressed in the equation:

s=k×Pgas

where s is solubility in M

k is Henry's constant in M/atm

P is the vapor pressure of the gas over the solution

Another way of explaining this is that higher pressures lead to greater force in collisions between the gas particles above the solution and the solution itself. Their average kinetic energy is greater, and their average speeds are greater.  So it is more likely that some of the particles will go into the solution and get dissolved.