A lot of guitar students have some confusion about the proper “shape” of the hand.
Hold your fretting hand out in front of you, palm up, and let the hand relax. Your fingers are likely to curl, pointing back up the arm, and your wrist will be basically straight. Now bend the hand upward at the wrist and open the fingers. The motion you just executed is the way your hand will move most naturally on the guitar neck: straight wrist and curled fingers vs. bent wrist and extended fingers, and most importantly the range of motion between these two extremes.
Consider that playing different things in different places require different amounts of finger extension.
Playing an open position C chord, for example, is different from playing a single C note on the first fret of the B string.
Playing an F note on the first fret on the high E string is different from playing F on the low E string. Since the finger has further to reach to get to a bass string, it needs to extend.
Now play your open position C chord and notice where your thumb falls on the back of the neck. The specific thumb placement depends on the proportions of your hand and the shape of the neck, but as a rule I find that open position chords work best with the thumb high. This straightens the wrist and curls the fingers, giving you more leverage and natural pressure on the strings.
Notice that your ring finger is more extended than the index.
This makes perfect sense: that 5th string C note under your ring finger is a larger reach than the 2nd string C note played by the index. You may also notice that while the index finger contacts the string at the fingertip, the extended ring finger is more likely contacting the string at least partially on the pad of the finger. Consider the difference in thickness and tension of the two strings, or treble and bass strings in general, and this should also make sense.
The extended finger on a bass string holds that thicker string down more efficiently…the larger surface area of the pad creates more pressure without your needing to push harder.
Try this exercise to illustrate this concept. Download the pdf here and watch the lesson video to hear the exercise played slowly and then up to speed. Remember, accuracy first, speed later….the opposite simply leads to sloppy playing and a fuzzy mental picture of what you’re doing. Start slowly and don’t pick up speed until you’re able to execute each move cleanly. Have fun!