Many pros continue to customize their racquet handles in various ways, and an easy, cheap way for the weekend player to do so is to swap out their stock, typically synthetic grip, and replace it with a leather grip to be used under an overgrip.  Why?  A leather grip under an overgrip gives better ball feel and racquet response, for several reasons. 

First, a leather grip is firmer and less cushiony than a synthetic grip, meaning that more of the good vibrations that come from a ball hitting the stringbed get transferred to your hitting hand.  This is especially true if you're used to wrapping an overgrip over a synthetic base grip - that's way too much cushioning for the typical player, and you're often left with a bulbous, rounded grip with diminished ball feel.  Keep in mind, not all racquet vibration is bad - anyone who's used (and been disappointed by) an overdampened, new-age racquet will tell you that.  Better ball feel tells you whether you've made solid contact on a shot, and that dictates your positioning in time for your next shot.  Hitting a solid shot just feels better with a leather, "lower to the ground" grip.

Second, a leather grip is more honest than a synthetic base grip.  Meaning, a leather grip will give you a truer feel for the actual size of your grip, and you'll feel the bevels of your grip more prominently with a leather grip, than with a synthetic grip.  This holds true even after one applies an overgrip over a leather base grip.  Since many players use different grips for many essential shots, one can see why being better able to define and feel out the grip's angles is a very good thing.

About 20 years ago, racquet makes began to innovate in the area of racquet handles, and this technology tipped with the introduction of Prince's Cushion Grip System - we still haven't recovered from that "innovation."  In addition to a synthetic base grip, Prince installed a rubbery handle base onto its top flight frames then, resulting in mushy handles that were nevertheless marketed as state of the art.  While this set-up may still make sense for sufferers of elbow woes, for the rest of us, I'd rather not be able to visibly squeeze down on a spongy handle!

Manufacturers have noticed, and replacement leather grips are readily available, ranging in price from about $7-12/each.  The leather grip generally regarded as the finest ever, the English-made Fairway calfskin grip, was previously discontinued, but that's actually not that big of a deal, because we're talking about a leather grip as a base grip, underneath a synthetic overgrip.  The Fairway's "Best Ever" qualities have everything to do with its leather-on-skin properties, and that's not a set-up I'm a fan of, personally.  All leather grips, when played with in direct contact, get slick rather quickly, and offer little actual grip or tack in sweaty conditions - in all honesty, the game has moved a bit beyond that particular set-up.

You should try leather under your overgrip.  You may like the different feeling.  Thanks for reading.