Go into the console (normally tilde key) and experiment with the following variables.
bob_pitch: The amount of movement that the player's screen moves up and down while in motion. Default 0.002
bob_roll: The amount of movement that the player's screen moves left and right while in motion. Default 0.002
bob_up: The amount of time before the player's screen starts moving. Default 0.005
You should leave them all at 0, or start at 0 and increase them 0.0001 at a time, testing if the movement makes you feel too bad.
Source:
Quake II console commands and variables