If I'd want to make it totally perfect then I gradually dim the extra LEDs, instead of taking just one value, but while testing I kind-a already liked it this way.

Hope this results in a better effect - I assume you'd try with adding 2 LEDs as in the code below, but you could most certainly try more.

Please note that this will only work with the FastLED library since we need to have the fadeLightBy function:

The full code:

#include "FastLED.h"
#define NUM_LEDS 60 // Total strip length
#define HALFLEDS 30 // One half LED count
CRGB leds[NUM_LEDS];
#define PIN 6 
void setup()
{
  FastLED.addLeds<WS2811, PIN, GRB>(leds, NUM_LEDS).setCorrection( TypicalLEDStrip );
}
//  REPLACE FROM HERE 
void loop() {
  byte colors[3][3] = { {0xff, 0,0}, 
                        {0xff, 0xff, 0xff}, 
                        {0   , 0   , 0xff} };
  BouncingColoredBalls(3, colors);
}
void BouncingColoredBalls(int BallCount, byte colors[][3]) {
  float Gravity = -9.81;
  int StartHeight = 1;
  
  float Height[BallCount];
  float ImpactVelocityStart = sqrt( -2 * Gravity * StartHeight );
  float ImpactVelocity[BallCount];
  float TimeSinceLastBounce[BallCount];
  int   Position[BallCount];
  long  ClockTimeSinceLastBounce[BallCount];
  float Dampening[BallCount];
  
  for (int i = 0 ; i < BallCount ; i++) {   
    ClockTimeSinceLastBounce = millis();
    Height = StartHeight;
    Position = 0; 
    ImpactVelocity = ImpactVelocityStart;
    TimeSinceLastBounce = 0;
    Dampening = 0.90 - float(i)/pow(BallCount,2); 
  }
  while (true) {
    for (int i = 0 ; i < BallCount ; i++) {
      TimeSinceLastBounce =  millis() - ClockTimeSinceLastBounce;
      Height = 0.5 * Gravity * pow( TimeSinceLastBounce/1000 , 2.0 ) + ImpactVelocity * TimeSinceLastBounce/1000;
  
      if ( Height < 0 ) {                      
        Height = 0;
        ImpactVelocity = Dampening * ImpactVelocity;
        ClockTimeSinceLastBounce = millis();
  
        if ( ImpactVelocity < 0.01 ) {
          ImpactVelocity = ImpactVelocityStart;
        }
      }
      Position = round( Height * (HALFLEDS - 1) / StartHeight);
    }
  
    for (int i = 0 ; i < BallCount ; i++) {
      // Leftside; (chnage 220 for dimming, and 2 for number of extra LEDs on each side)
      DrawBall(Position,colors[0],colors[1],colors[2], 220, 2);
      // Rightside;
      DrawBall(NUM_LEDS-Position-1,colors[0],colors[1],colors[2], 220, 2);
    }
    
    showStrip();
    setAll(0,0,0);
  }
}
void DrawBall(int ballPosition, byte red, byte green, byte blue, byte dimming, byte ExtraSidePixelCount) {
  // LEDs before the center LED
  for(int counter=1; counter<=ExtraSidePixelCount; counter++) {
    if(ballPosition-counter>=0) { 
      setPixel(ballPosition-counter,red,green,blue); 
      leds[ballPosition-counter].fadeLightBy( dimming ); 
    }
  }
  
  // Center LED    
  setPixel(ballPosition,red,green,blue);
  
  // LEDs after the center LED
  for(int counter=1; counter<=ExtraSidePixelCount; counter++) {    
    if(ballPosition+counter<HALFLEDS) { 
      setPixel(ballPosition+counter,red,green,blue); 
      leds[ballPosition+counter].fadeLightBy( dimming ); 
    }
  }
}
//  REPLACE TO HERE 
void showStrip() {
 #ifdef ADAFRUIT_NEOPIXEL_H 
   // NeoPixel
   strip.show();
 #endif
 #ifndef ADAFRUIT_NEOPIXEL_H
   // FastLED
   FastLED.show();
 #endif
}
void setPixel(int Pixel, byte red, byte green, byte blue) {
 #ifdef ADAFRUIT_NEOPIXEL_H 
   // NeoPixel
   strip.setPixelColor(Pixel, strip.Color(red, green, blue));
 #endif
 #ifndef ADAFRUIT_NEOPIXEL_H 
   // FastLED
   leds[Pixel].r = red;
   leds[Pixel].g = green;
   leds[Pixel].b = blue;
 #endif
}
void setAll(byte red, byte green, byte blue) {
  for(int i = 0; i < NUM_LEDS; i++ ) {
    setPixel(i, red, green, blue); 
  }
  showStrip();
}