It's not uncommon to hear the advice to put weight on your left side for short shots, and to respond by sliding only your lower body toward the target. It's a common, and costly, fault. By shifting only your hips, your upper body and head tilt back behind the ball, causing the club to bottom out too soon and resulting in fat or thin contact.
The proper way to address short shots is to lean your entire body toward the target, so your eyes are ahead of the ball. You can check this by hanging a club straight down from your right eyeyou should see the clubhead pointing down in front of the ball. This moves your center of gravity forward, promoting the sharp, descending blow you want on chips and pitches.