Higher viscosity shock oils take more time to flow through the holes in the shock pistons and therefore slow down the transition time for that corner of the car. Lighter oil will let the car transition faster. Finding the right balance is what chassis tuning is all about. You can also tune the shocks (sometimes called dampeners) by changing the piston in the shock to have more holes or larger holes.
Also, remember that the springs control how much travel you will have for a specific load and the shocks control the speed of the transition. If have too soft of a spring, you can't hold the car up with heaver shock oil.
Hope that helps.
AKA Big Bad Bob