Circumstances which amount to  REASONABLE SUSPICION to detain and investigate are defined as circumstances which are less than those necessary for arrest. They constitute a "reasonable, articulable suspicion that a particular person had committed, was committing, or was about to commit a crime."  

In the context of a DUI case, this means that if a police officer sees someone weaving from lane to lane, it is reasonable for the officer to assume that the driver may be driving under the influence and he has a reason for, or a "reasonable suspicion", to justify stopping  the car to investigate.