For aspiration of gastric volumes we would use a smaller syringe (5 ml) unless you expect a volume of 20 ml or so.
In terms of physics, I think you must differentiate between positive pressure and negative pressure. If you push the piston of a syringe forwards the force that you exert is pressure divided by diameter of the piston. However, the negative pressure that you apply is simply the amount of vacuum in the syringe. If you pull the piston back by the same distance (for instance 6mm) you get a higher vacuum and a higher negative pressure in a 10 ml syringe (with a bigger piston) than